There's a regular pentagon in the middle of the star, which equals 180 * 3 = 540 Then each of the angle in the pentagon is 108. As we see, each angle involved in the diagram were actually in the same isosceles triangles. So, we take out the straight line 180 - 108 = 72 which is an angle of the isosceles triangle. Nextly, add up the angles by itself and subtract by 180 to get the angle alpha 180 - (72 + 72) = 36 There are 5 same angles in the star which is 36 so 36 * 5 = 180 equivalent to a + b + c + d + e = 180 Thank you.
@tiresias3342
5 жыл бұрын
Aidil Shazwan that's what I did too
@_omri_
5 жыл бұрын
Lmfao that's what I did and this dude wants to talk about rotation and ish
@SD-po6hk
5 жыл бұрын
True👍🏻
@piyalikarmakar5099
5 жыл бұрын
yes it is the same method i used.
@sagarhande1891
5 жыл бұрын
I solved with the help of regular pentagon too
@hxppy650
5 жыл бұрын
Perhaps one of the easiest problems you've solved so far
@mukultiwari2339
4 жыл бұрын
Ya of course 😊
@teddanville6996
4 жыл бұрын
it’s for 13 years old, get real, there’s a lower chance that a 13 years old can solve this.
@gerentlee
4 жыл бұрын
Ted Danville lol I was taught about this at 13 years old and I thought it was not hard. It might be a bit hard without knowing ext. angle of triangle
@ch-bf6dw
4 жыл бұрын
@@teddanville6996 In India, many 8th grade students learn 10th grade geometry
@archeopterixneuroza4715
4 жыл бұрын
@@teddanville6996 We have pretty shitty Math in my country, nevertheless 13 year old should be able to solve it 🤣 Like it's absolutely basic...
@Aorda
3 жыл бұрын
One of the problems I solved looking at the thumbnail!
@olivermiller8943
3 жыл бұрын
Same
@sofiking3729
3 жыл бұрын
yup
@jakobj55
3 жыл бұрын
weird flex
@jannes3290
3 жыл бұрын
Same
@RandomPerson-sh9tu
3 жыл бұрын
same, and we're not really trying to flex, it's probably just the first time we've been able to solve a problem just from the thumbnail, it's certainly a first for me.
@praveenkumars4243
5 жыл бұрын
I used the Pentagon in between. Sum of it is 540°. Then did some basic stuffs and in the end arrived at 180°
@Wootsk
5 жыл бұрын
I also used the Pentagon. But as I do not remember much formulae beside angle in triangle is 180, I spilt it into 5 triangle to calculate a side.
@merveilmeok2416
5 жыл бұрын
LOL@ “basic stuff”. You get extra credit for creative use of language.
@abodalashkar5686
5 жыл бұрын
I did the same
@aizatsukor3359
5 жыл бұрын
@@merveilmeok2416 it is pretty basic stuff actually... thats why it's for form 1 or 13y/o
@omaraliev896
5 жыл бұрын
I did it the same
@strictlyeducationalmagick
5 жыл бұрын
Do you realize you just unwittingly summoned demons from hell.
@rish_hyun
5 жыл бұрын
What do you mean!
@y0shiness
5 жыл бұрын
@@rish_hyun satanic pentagram at 3:03
@rish_hyun
5 жыл бұрын
@@y0shiness ohh!
@jeffreyblack666
5 жыл бұрын
What makes you think it was unwittingly?
@whitegx-k5i
5 жыл бұрын
i can graph a pentagram on my TI-84(but i have to draw the circle)
@duncandonnchadh6721
3 жыл бұрын
The intuitive explanation is so amazingly simple and elegant, i just lost it for a second.
@indisputablefacts8507
3 жыл бұрын
I'm a bit boggled that he says it's not a proof - it is a proof, not only of the regular star but the irregular one as well.
@thepetyo
3 жыл бұрын
@@indisputablefacts8507 And it is far too complicated to get the intuitive result.
@OliverChristensen-i4u
2 жыл бұрын
@@creamwobbly Can you elaborate on why that is not a proof (the 5x5=25)? To my knowledge, a proof uses definitions to transform the original statement into another statement that has been proven before. Here, the definition of 5x5 given by 5+5+5+5+5 which already has been proven to be 25.
@Chris-hf2sl
Ай бұрын
@@indisputablefacts8507 Yes, if you think of the arrows being rotating vectors, then clearly since the vector is rotated by 180º, the sum of each of the angles used in that rotation must be 180º. But I solved it in a different way: Draw a line between the two bottom vertices, parallel to the existing horizontal line and then consider the new triangle that this new line forms with the vertex at the top. This includes the angles a, d and c (as labeled at 0:17 in the video) plus two new angles at the bottom. But these two new angles equal b and e (since we have lines crossing two parallel lines). So the total of all the angles in this new triangle is a+b+c+d+e, which like all triangles = 180º.
@AmbyAxolotl
4 жыл бұрын
4:16 now that's a star I drew when I was 3 lol
@nadarmt7069
4 жыл бұрын
I ruined the 69, sorry
@AmbyAxolotl
4 жыл бұрын
@@nadarmt7069 nah I got you fam
@urano4810
4 жыл бұрын
Do your stars look any better now?
@AmbyAxolotl
4 жыл бұрын
@@urano4810 nope lol
@powerflame
4 жыл бұрын
100th liek
@chiragmantri4947
5 жыл бұрын
Who thinks that these videos are getting easier and easier by the new one🤔🙄?
@soelinhtet6064
5 жыл бұрын
i agree
@johnnastrom9400
5 жыл бұрын
They are not. People like to make that claim in an effort to make themselves look more intelligent than they really are. And I doubt that a 13-year old could do this without preparation as is always implied.
@piyalikarmakar5099
5 жыл бұрын
a 13 year-old can do this but in some different method..... @@johnnastrom9400
@sabyasachirimpa
5 жыл бұрын
Some guys are not gifted with Einstein intelligence like you.
@chiragmantri4947
5 жыл бұрын
Hey guyz i was trying to say that Presh posted tricky and interesting problems But these are bookish ones(nowadays)🤥😟😕😏🙏
@Devo491
3 жыл бұрын
I followed the geometry route, working from the inner pentagon, and got it right :) But your alternative methods really opened my eyes. Outside the square can be very rewarding.
@guts1859
2 жыл бұрын
I did the same approach as you
@TheOfficialCzex
5 жыл бұрын
180(n-2) where 'n' is equal to the number of sides of the regular pentagon gives us 540 540/5 angles is 108 The supplementary angle of 108 is 72 2 interior angles of the triangle multiplied by 72 give us 144 180 degrees of the interior of a triangle minus 144 leaves 36 degrees for a, b, c, d, and e 36 by the 5 interior angles of the triangles is 180 180 degrees
@Nalkahn
5 жыл бұрын
Did it this way too
@TrojanCommander
5 жыл бұрын
This is the easier method
@natalieeuley1734
5 жыл бұрын
Yep, that's what I did
@Nalkahn
5 жыл бұрын
@Nshsls Snshshsj thx captain
@jeffreyblack666
5 жыл бұрын
@Nshsls Snshshsj This way is a lot easier to generalise (by extending it) to any case, including other number of sides. You have n triangles which each have an angle sum of 180 degrees, where 2 of the angle are made up of the exterior angles of the shape, and the sum of the exterior angles is always 360 degrees. Thus the angle sum would be n*180-2*360=180*(n-4)
@EdwardNo1
5 жыл бұрын
3:08 that's the reason why I'm here
@andrewkosmowski3985
4 жыл бұрын
I worked in reverse from your first proof on the regular stellated pentagon. I put the pentagon in the circle. A circle has 360 degrees, so the pentagon must have 5 360/5 angles, so each is 72. I knew the point of the isosceles triangle of the stellated pentagon is half of this, thus 36. So, 36 x 5 equals 180.
@ОскарПитерсон-я7г
2 жыл бұрын
lol that’s what I’ve thought of straightaway, too
@ronalddump4061
2 жыл бұрын
Keep it simple. A pentagon can be divided into 3 triangles. That equals 540 degrees total. Divide by 5, Each angle of the pentagon is thus 108 deg. In the triangle, the small (point angle) is thus 36 deg. (180 - 72 - 72 = 36.) 36 x 5 is 180
@micah2936
Жыл бұрын
@@ronalddump4061you guys give me a headache by assuming the pentagon is symmetrical……. Angles in a pentagon can also be 100, 90, 115, 117, and 118 🤷♂️ as soon as you assume it’s not irregular your proof is broken and will not apply to all situations. I know it’s still the same end result, but a proof being correct doesn’t rely on end results, it relies on being compatible for every possible situation.
@evank3718
5 жыл бұрын
3:10 Whoaaa okay there. This is geometry not a demonic cult.
@orngng
4 жыл бұрын
Just to let you know it's a Patan pentagram The star is pointing up and not down therefore it's not a demonic pentagram
@umhello9962
4 жыл бұрын
Izaak I think they were joking-
@orngng
4 жыл бұрын
Um Hello yes about him trying to be a satanist no for not knowing specifically what the symbol is
@justanotherweirdo11
4 жыл бұрын
@@umhello9962 It's just not funny because it's inaccurate.
@briankenney9528
4 жыл бұрын
Aw heck. I signed up for the demonic cult
@rajneedwivedi1453
5 жыл бұрын
It can be solved in nearly 10seconds by applying exterior angle rule That's the easiest according to me
@Blayz705
4 жыл бұрын
Rajnee Dwivedi and vertical angles thm
@anandk9220
4 жыл бұрын
That's true. 👍
@mcwulf25
4 жыл бұрын
Me too
@stanbest3743
4 жыл бұрын
Of course, much easier than working from the sum of the interior angles, which I did.
@DharmendraKumar-he6mp
4 жыл бұрын
Yo bro
@_Some_Guy_
3 жыл бұрын
i imagined walking around the star from start to finish and counted 2 full revolutions along this path (720 degrees). Therefore the exterior angle at each point is (720/5) =144 degrees. Therefore the interior angle at each point is (180-144) = 36 degrees. Therefore the sum of all 5 angles would be (36x5) = 180 degrees.
@jrunsvold
2 жыл бұрын
Same! 🙌
@ceciliapreziose3783
Жыл бұрын
@ceciliapreziose3783 0 seconds ago so I saw that these triangles are equilateral. angle degree is app 33% x 5 = 165, app
@theyouuser
5 жыл бұрын
One of the easier ones, managed from the thumbnail. Love these little puzzles.
@addityasinghal897
5 жыл бұрын
Simple exterior angle property! And end it with a lovely Angle sum property!
@amango6297
3 жыл бұрын
This is that question who give me a chocolate 🍫 form my teacher for solving this in my 8th class I can't forget that movement 🙂
@jeftesantiago
3 жыл бұрын
I do not forget moments like that neither.
@HimanshuGrv
3 жыл бұрын
@@jeftesantiago Liked the way you corrected him😉
@hellboy7014
3 жыл бұрын
@@HimanshuGrv he didn't 😒
@machomachinmachinmachinmac6910
3 жыл бұрын
Let me translate this for you : "This is the question that resulted in me being rewarded by my teacher for solving it in my 8th year of school. That moment was unforgettable".
@jeftesantiago
3 жыл бұрын
@@machomachinmachinmachinmac6910 It is all about formal or informal writing. Probably, if you were in college you learned a lot there. I just prefer formal writing in most of my writing journeys.
@RubyPiec
5 жыл бұрын
got it! the answer is a number between 0 and 360!
@johlene1813
4 жыл бұрын
Agree. The sum of all the angles is 360
@NarutoUzumaki-xd4db
3 жыл бұрын
Why you used (!) . This know as factorial which is used in permutations and combinations
@RubyPiec
3 жыл бұрын
@@NarutoUzumaki-xd4db I am a failure to all mathematicians.
xXFazeNoScoper360DoesNoScopes420BlazeItXxYYzPS4HD math usually is
@1trucxhondamov589
5 жыл бұрын
Your everywhere!
@JohnSmith-kj2od
3 жыл бұрын
As an Indian I've seen this question so many times that I knew the answer by heart
@playerscience
3 жыл бұрын
John Smith me too.
@Sayandip
3 жыл бұрын
Lol mee too 😂😂
@pianopianist5709
3 жыл бұрын
I was asked this question when I was in 5th grade, that is when I was 9. Since then, I have seen this problem so so so so so many times.
@pianopianist5709
3 жыл бұрын
@Aadi Ringay Sorry, I meant 9, that was a mistake
@isaacshiellsthomas992
5 жыл бұрын
Commence devil summoning at 3:09 ...
@leeladhar7468
4 жыл бұрын
Imagine solving random pentagon questions and suddenly u see satan sitting in front of u
@sutfolsemaj
5 жыл бұрын
The sum of the angles in a pentagon (regular or irregular) is always 540 degrees. The sum of the angles of 5 triangles will be equal to 900 degrees. The sum of all ten of the exterior angles of a pentagon is equal to 720 degrees. Since each triangle is constructed by 2 exterior angles of the pentagon and some 3rd angle which we do not know, we can extrapolate that the sum of those 5 angles must be equal to 180 degrees by realizing that the ten exterior angles (720) plus the 5 unknown angles must add up to the total angles of the triangles (900).
@alessandropizzotti932
5 жыл бұрын
That's right, and it's indeed the simplest way to prove the result, but what have the "areas" got to do with it all?
@bh8642
5 жыл бұрын
+AP. I think it's a typo and he meant angles not area.
@sutfolsemaj
5 жыл бұрын
Yeah, that's what I get for typing it on my phone lol
@shenanigans4177
5 жыл бұрын
Thats just over complication to the sky.... It hardly took 5 sec for me to solve. Let me explain Exterior angle sum property of triangle. So 5x = 180, x is the angle on each corner.
@thuglife1219
Жыл бұрын
As a 14 year old currently who has recently been exposed to such high level questions (Mainly from Olympiads) I can confirm that this is true
@brainboxanky1729
5 жыл бұрын
Well this came in my exams And the solution I then had was too long Theese soln are freaking easy and awesome Wish this video had been available then
@flpdragonslayersmith8
3 жыл бұрын
Dude its been so long since I've used geometry or trigonometry that I can't remember. Thanks for refreshing the ol brain sir.
@seanleith5312
3 жыл бұрын
India? He should post math questions from Uganda.
@codernakul
3 жыл бұрын
@@seanleith5312 Umm What do you mean by that does Uganda have even more difficult questions?
@zeeshanmuqtadeer2459
3 жыл бұрын
Crew : Views are low! What to do? Head : Time for the INDIA CARD!
@ampo5671
3 жыл бұрын
😂😂😂..so true
@bylebree4842
4 жыл бұрын
That was so complicated process took me like a minute mentally?
@JustJum
5 жыл бұрын
I only saw the first 20 seconds of the video. I did the calculations in my head (because im too lazy to get a calculator or paper) and the answer is 180. Edit: i watched the video and damn... he went waaaay too deep into it. I just did some basic sums
@Ryuk-apples
3 жыл бұрын
I am proud of myself even if it took me 10 min hahaha im 30 btw 💀💀
@sanjibghosh3373
5 жыл бұрын
I got this problem when I was in 6th grade in India and it was a MCQ of marks 1/4 🤣🤣
@apratimtewari4288
3 жыл бұрын
We got ALMOST the same name
@pianopianist5709
3 жыл бұрын
5th Grae
@Dorddis
5 жыл бұрын
I got 300 as an answer..... WELL I TRIED
@forestreee
5 жыл бұрын
I know how you got 300. You thought that each triangle outside the Pentagon must be an equilateral triangle so you thought that each angle a, b, c, d, e is 60 degrees so you did 60*5 = 300. Right?
@voidl_rd
5 жыл бұрын
i got stockholm
@sycorax2029
5 жыл бұрын
Omg i got that answer too
@0megazeero
4 жыл бұрын
Still better than me I got Neptune
@supercool1312
4 жыл бұрын
Siddharth Rodrigues i got 360
@puspamadak
3 жыл бұрын
The last method was great! That completely went out of my mind.
@piyush-kx6vi
3 жыл бұрын
right!!!
@babyyoda5074
5 жыл бұрын
This question had a simple solution which includes the pentagon in between. But thanks a lot for giving us a lot of new stuff. This is an amazing channel.
@mirrorsreflectyou6302
4 жыл бұрын
That simple solution is possible only if it's a regular Pentagon
@gobinnishad
3 жыл бұрын
Even more simple when you use exterior angle property of triangle.
@ClikcerProductions
3 жыл бұрын
@@mirrorsreflectyou6302 It does not need to be a regular pentagon for using the pentagon to be the easy way to solve this at all, the exterior angles will always be 360 which very quickly makes it clear that its 180
@randomcontentgirl8182
4 жыл бұрын
According to a 9 year old's answer(Me) Every triangle has an angle of 45 cos its right triangle angles so 45 x 5 is 225
@hloi7013
3 жыл бұрын
I remember When I was in 7th grade, This was my one of my exam question..
@Prs722
5 жыл бұрын
Presh you really over complicated this one
@bas2362
4 жыл бұрын
I've been bingeing videos lately and have found myself finding a lot of these answers just from thinking about it. Guess college taught me to think about maths in a different way than high school.
@99bobcain
3 жыл бұрын
Its more important to learn and understand how to reason out the answer. The solution will get you past the test, the process will get you through life.
@sechi7239
3 жыл бұрын
A simpler solution yet is to imagine a particle starting out along one of the lines making a series of right turns (five in total) of a + b + c + d + e degrees. It will end up going in the exact opposite direction in order to be able to reach the corner where it began. Or, more formally, take a unit vector parallel to the line segment AC. If one rotates it a + b + c + d + e degrees we end up with the unit vector -AC (minus AC).
@sakarasomapa
5 жыл бұрын
For the asymmetry ones I do it like this. Declare name for angle inside the pentagon a’ to e’ and find each angle. a = 180 - (180-c’) - (180-d’) a = c’ + d’ - 180 The rest of the angle will work the same way (but gives different new angle) and after summing it up we’d get a+b+c+d+e = 2a’+2b’+2c’+2d’+2e’ - 900 The sum of angle in a pentagon = 180*(5-2) = 540 a+b+c+d+e = 2(540) - 900 = 180 I try to use as basic ways as possible at first but I realize I’d have to use sum of inner shape anyway after some point and since I’m too lazy to scrape it and redo the whole thing I just went with it.
@pandachong7942
5 жыл бұрын
Outer angles of shapes always add up to 360. It’s a pentagon so it has 5 outer angles. 72 + 72 is 144. 36 x 5 is 180
@sofiejosefsen242
4 жыл бұрын
My answer is: 180/5=36 degrees
@ronalddump4061
2 жыл бұрын
The outer angles of a pentagon is obviously 360 minis 108 = 252 deg. 252 deg x 5 = 1260 deg You are going to need to be more clear about what you mean by "the outer angles of shapes"
@payalsanghi3170
2 жыл бұрын
There could be a simpler method @MindYourDecisions: The sum of external angles of a pentagon is 360° and in all the triangles there are 2 external angles of pentagon coming from different directions. So, sum of all those angles in 5 triangles is 720°(=360°*2). Sum of all the angles of five triangles is 900°( =180°*5). Therefore, a + b + c + d + e = 900° - 720° = 180°.
@Novasky2007
5 жыл бұрын
Triangle = 180° 360/5=72 72/2= 36 72+72+36=180° Each point is 36° 36 x 5 = 180 Or just 360/10 = 36
@granadierfc1953
5 жыл бұрын
This question appeared in ANTHE
@Lalasfritas
4 жыл бұрын
Use exterior angle formula 360/n, which in this case equals 72. You can do this for the other angle as well. Use the triangle angle sum theorem, meaning 72+72=144, then 180-144= 36. Then multiply 36 by 5 because there are 5 vertices, resulting in 180°.
@xz1891
5 жыл бұрын
π in 0.1 sec. Anyone if interested, I'd explain.
@Bozzigmupp
4 жыл бұрын
X Z what
@xz1891
4 жыл бұрын
Those five angles are equal, and are Circumferential ones, so we know their corresponding Central angles are twice of them. While all these central angles corresponds an exact circle, so the summation is 2π, thus the summed circumferential angles are half of it, that is π, i.e. 180°, with each being 36°.
@zachbarry1992
5 жыл бұрын
Easiest way to prove it - 1) pentagon consists of a quadrilateral and a triangle, and quadrilateral has 360 degrees and triangle has 180 degrees (angles measures added up) 2) that means each angle of a perfect pentagon is 108 degrees 3) that means that the two angles at the base of the five outer isosceles triangles are 72 degrees because of supplementary angles (180-108=72) 4) if two of the angles of the outer triangles are 72 then the last angle must me 36 degrees (180 - (2•73)=36) 5) for all of the five angles - 36 • 5 equals 180
@nicholasschroeder3678
4 жыл бұрын
I took math through 3rd semester calculus...these things make me want to take it up again.
@yeung1216
5 жыл бұрын
The easiest way is to do triangle exterior angle . for example the small triangle of the top. The bottom left corner will b+d and the bottom right will be c+e and a triangle have 180 so abcde sum will be 180
@parttroll1
5 жыл бұрын
That's the way I did it 'Z' angles when you have a line parallel to each other
@indirawalavalkar1972
4 жыл бұрын
an exterior angle theorem is the easiest way
@safinahammed4391
3 жыл бұрын
Exactly ☺️
@lostfeather1089
5 жыл бұрын
This question was in my mathematics book in 8th grade :)
@lostfeather1089
5 жыл бұрын
@Seema Singh 😉😉
@mridulabajpai334
4 жыл бұрын
Nope.. it is from grade 7 R S Aggarwal textbook
@PIANOSTYLE100
3 жыл бұрын
I ll have to study this a bit.
@PIANOSTYLE100
3 жыл бұрын
I am kinda hooked..Wish I had this stuff in college.
@parvezmakandar4269
4 жыл бұрын
Who else felt proud after solving the problem and then felt ashamed cuz its solved by 13 year olds
@arkancer2210
4 жыл бұрын
13 year old in high shool, couldn't do it. Probably because I never truly passed geometry.
@the-wv6wx
5 жыл бұрын
this was in my year end exam in Hong Kong last year
@numbereightyseven
3 жыл бұрын
Everyone's saying how easy this was, but remember, it was set for 13-year-olds, and I doubt they were trying to trick them. So well done all you Einsteins.
@michelbruns
3 жыл бұрын
When i was 13 we had geometry the very first time in school, everyone saying "we had this in 2th grade" is saying bs
@goldenfish1014
5 жыл бұрын
i did this in 15 seconds :D
@dhilonstephan
4 жыл бұрын
Same
@subswithvideos-io1vx
4 жыл бұрын
Same using the pentagon
@rahimeozsoy4244
4 жыл бұрын
How?
@sourikpaul8953
5 жыл бұрын
There's a simple formula. (n-4)π
@piyalikarmakar5099
5 жыл бұрын
it is (n-2)π
@jagmarz
5 жыл бұрын
@@piyalikarmakar5099 I think the confusion is sum of interior angles of an n-gon vs the sum of the star points inscribed in that polygon. Consider a hexagon. Inscribing a star (of David) in one, will give you two equilateral triangles or 360 degrees [(n-4)*180] when you sum the points. But the total of the interior angles is 720 [(n-2)*180]. So they are separate and distinct formulas.
@jagmarz
5 жыл бұрын
@@piyalikarmakar5099 Yes, but the the formulas also apply for a hexagon. I was just using a different example to illustrate that the (n-2)*180 and (n-4)*180 are both valid, but measure different things.
@sourikpaul8953
5 жыл бұрын
I searched this online. If n is the number of sides of the star, then the sum of the angles will be (n-4)180.
@jeffreyblack666
5 жыл бұрын
@@piyalikarmakar5099 It will be vastly different. n is 5. 5-2 is 3. 3 pi in degrees will be 540 degrees. That is quite different to 180 degrees. As for the case of a triangle, you can't make a star from a triangle as the lines diverge. You are thinking of the angle sum of the pentagon (or an n sided shape) itself.
@payalsanghi3170
2 жыл бұрын
There could be a simpler method @MindYourDecisions: The sum of external angles of a pentagon is 360° and in all the triangles there are 2 external angles of pentagon coming from different directions. So, sum of all those angles in 5 triangles is 720°(=360°*2). Sum of all the angles of five triangles is 900°( =180°*5). Therefore, a + b + c + d + e = 900° - 720° = 180°.
@saulleonardorodriguezsolis8694
5 жыл бұрын
I put every triangle next to the other. Then, I found the semi circle. That's means there's a 180°
@kevinkang8299
4 жыл бұрын
nice way LOL
@swapnil3990
5 жыл бұрын
Needlessly lengthy solution. Here's the very short one: The Pentagon in centre is regular, each angle 108°. The Pentagon has 5 isosceles triangles on each side. That gives us the equal angles of the triangle = 72°. Thus each corner angle is 36°. This is how it was supposed to be solved.
@usedtoilet8295
5 жыл бұрын
Well I kinda started with that as well but that wouldn't be really mathematical though isn't it
@rg1346
5 жыл бұрын
That's a boring solution
@swapnil3990
5 жыл бұрын
@@rg1346 Clearly smart is always boring
@engaged5037
4 жыл бұрын
It can be done more easily by applying exterior angle rule
@ameyakathale4992
4 жыл бұрын
Hit like if you see the Pentagon 👍👍 And also used interior angles to get the answer😁😁
@RanjanKumar-cs2yg
5 жыл бұрын
hey this is precious tall stalker..!!! hhhahahaha
@yuck9510
3 жыл бұрын
hahaha that was so funny! please make more funny jokesss!!!
@alster724
2 жыл бұрын
This is easy First let's label the pentagon's interior angles as a1,a2,a3,a4, and a5. and the star's corners as A,B,C,D, and E The sum of the interior angles are Si= 180(5-2) -> 540° We can form 5 possible triangles using interior angles only Namely a1+C+D =180° a2+B+E=180° a3+A+E = 180° a4+A+D= 180° a5+B+C = 180° Adding them all uo we get 2(A+B+C+D+E)+(a1+a2+a3+a4+a5)= 900° But we all know a1+a2+a3+a4+a5 = Si (Pentagon) = 540° 2(A+B+C+D+E)+540=900° A+B+C+D+E+270= 450° A+B+C+D+E= 180°
@GrassToucher988
4 жыл бұрын
Me after seeing the thumbnail: *open Google* Me: "pEnTaGoN aNgLe"
@lingling2823
4 жыл бұрын
PunBreakerz Channel I had to search up the formula for finding interior angles cause I forgot lmfao... (n-2)180
@lordman5497
5 жыл бұрын
3:13 Villager noise
@rahimeozsoy4244
4 жыл бұрын
xDD
@alexandreman8601
3 жыл бұрын
4:25 I don't get it. Why is the exterior angle equal to b + d?
@Tushar_Sinha
3 жыл бұрын
The sum of the three angles in a triangle is 180 degrees. Let us assume the third angle in the triangle highlighted as x. So b+d+x=180. Now the exterior angle + x = 180, as they both lie on a same straight line. So, exterior angle + (180 - b - d) = 180. Therefore, exterior angle = b+d. This holds true for all exterior angles to a triangle. Hope that answers your question.
@lokeshnagasaikumar.molleti9097
3 жыл бұрын
@@Tushar_Sinha Thank you bro I too have the same doubt.
@edinssonleonardo
5 жыл бұрын
Saludos de Colombia, genial su trabajo!
@vuraxis953
5 жыл бұрын
I solved this in about 30 seconds.
@rao8559
4 жыл бұрын
Give yourself a medal
@supercool1312
4 жыл бұрын
i got it as 360, by figuring out that all the angles add up to 1440, and they equal 5(360-2a)+5a, as the angle opposite each one on the outside equals 2a, so the one inside must be 360-2a., then making it 1800-5a=1440, thus 5a=360, and a=72
@HarshG28
5 жыл бұрын
Yeah this is in my assignment booklet I am from India And 14 yr old
@Dkmasteris
3 жыл бұрын
Step one: take a protractor Step two: Measure the corners Step three: add them up Step four: Bask in the misery of others!
@nagubaikadapa7761
3 жыл бұрын
Legends like us do that and end up getting 353.89 degrees👍
@HansBezemer
3 жыл бұрын
Since the center is a regular pentagon, the total of its corners are 540 deg. 540 deg / 5 corners = 108 deg. Hence, since it's built from regular triangles, the other corners are 180 deg - 108 deg = 72 deg. A single corner is 36 deg. 5 times 36 deg = 180 deg.
@koishi8361
4 жыл бұрын
When he stated to draw an arrow, I was like "Damn would have used a circle.." xD And for the 2nd the the intercept theorem. Well :D
@debkamalsarkar1521
3 жыл бұрын
I also had this one when I was 13😂😂😂 Everybody has to do such questions 😂
@supex234
3 жыл бұрын
Your method of solving this is something what my math's teacher named overthinking (for regular pentagon).
@GurpreetSingh-zu7vv
5 жыл бұрын
No one can challenge Indians in math
@ibrahimtouman2279
5 жыл бұрын
Sorry to tell you, but I never heard of any great Indian mathematician
@francisxes8471
5 жыл бұрын
Ibrahim Touman Srinivasa Ramanujan?
@jaideepshekhar4621
5 жыл бұрын
Aryabhatta?
@jaideepshekhar4621
5 жыл бұрын
Brahmagupta?
@jaideepshekhar4621
5 жыл бұрын
Bhaskaracharya?
@Saurabhkumar-vy5uo
5 жыл бұрын
Yeah I remember my childhood days when we used to get these questions in tests .
@tonyshen7478
4 жыл бұрын
Assuming the 5 inner corners of the pentagon in the middle as f, g, h, i, j. It's easy to know that f+g+h+i+j=540. Also, a=180-(180-f)-(180-g)=f+g-180, b=180-(180-g)-(180-h)=g+h-180, c=180-(180-h)-(180-i)=h+i-180, d=180-(180-i)-(180-j)=i+j-180, e=180-(180-j)-(180-f)=j+f-180, So, a+b+c+d+e= 2(f+g+h+i+j)-900=2*540-900=180 Therefore, no matter what a, b, c, d and e are respecitively, their sum is always 180.
@jimarious6616
5 жыл бұрын
3:02 lul
@charumodi2326
5 жыл бұрын
I got it easily... The answer is 180... If it came in my test i gotta top..
@aslamkhan-vl2we
5 жыл бұрын
U are thinking only u can solve it so fast?
@victherocker
5 жыл бұрын
that's why it's for *13-year-old*
@jonasthemovie
5 жыл бұрын
Proof?
@charumodi2326
5 жыл бұрын
@@jonasthemovie Why the hell do i need to prove you anything? U don't wanna believe don't... I dont care...
@jonasthemovie
5 жыл бұрын
@@charumodi2326 The task was to solve and prove. How would you top such a test?
@letstalksciencewithshashwa9527
2 жыл бұрын
Sir i have another way... We can make a line cd parallel to be ...then with alternate interior angles the figure acd is a triangle and hence the sum of angles in 180.... I am an Indian student who got this in my school exam
@Limondero
5 жыл бұрын
*_EASIEST way for ANY 5-pointed star_* For every corner we have 180 - (180-x) - (180-y). Where x and y is corers inside pentagon. That means that for all corners we have 180x5 - 180*10 + 5x + 5y. 900 - 1800 + 540 + 540 = 180 That was easy, huh?
@gregoryashton
5 жыл бұрын
I’ve noticed that KZitemrs are saying “Subscribe for free” a lot more often now and it’s really starting to grind my gears ⚙️😖
@turtleneckless
5 жыл бұрын
Hes talking about patrion
@VishalSingh-nn4ne
3 жыл бұрын
Since it is a regular star , there will be a regular pentagon inside it , each angle of a regular pentagon is 108 deg then we have to use one of the triangle let's take upper triangle having angle 'a' then a+72+72=180 deg ( by using linear pair angle) then we get a= 36 Similarly for all remaining 4 angles Each angle is equal to 36deg a+b+c+d+e= 180 deg..
@fos1451
5 жыл бұрын
My answer will be PS = pointed star So = 5×PS = 5PS
@thomasthun
5 жыл бұрын
I loved math as a kid/college and you make me want to do this everyday again. Great work!
@idontneedthis388
3 жыл бұрын
Easy and elegant solution. Just draw the line from 'd' to 'c'. Then let give the name to dot where line 'e-c' intercepts line 'd-b', let's name it 'z'. Now you can see two triangles: 'adc' + 'ezb' = 360. Now you need to extract angle 'eZb' and angles 'zDc' and 'zCd'. Obviously angle 'eZb' is equals angle 'dZc', so you can extract 'zDc', 'zCd', 'dZc' and this is triangle, 180. 360 - 180 - 180!
@安荣-f5g
5 жыл бұрын
This video in one formula: Sum=5(180-2(180-(180(5-2)/5))) Why's this on KZitem? It's only tricky for 6th graders in China...
@Rahul-ge8ff
5 жыл бұрын
And 8th grade in India. I don't know who gave this as a challenge?
@lastmanstanding153
5 жыл бұрын
You third world coutries are so smart. /s
@lastmanstanding153
5 жыл бұрын
@@安荣-f5g Yet we created everything that allowed our species to evolve. As a matter of fact you wouldn't even be watching this video without us. Please, go back in your caves.
@安荣-f5g
5 жыл бұрын
Lastman Standing All I meant to say is to stop ur poor sarcasm, but it just got even worse. Guess ur a little 10yrs old new to the world right? Time to learn things
If anyone want to feel mathematics,, not to learn, the there is a book called mathwonders, this book is extraordinary, try it out
@igxniisan6996
3 жыл бұрын
Now try problems from JEE ADVANCE exams in india. :)
@armannikoghosyan1345
5 жыл бұрын
I solved this when i was 15..now Im 25..very easy
@jabachakraborty8803
4 жыл бұрын
Since,in a ∆sum of all angles are 180° & in a quadrilateral it 360° Then,180°-(a+d+180°-(e+c+180°-(b+d)+e=360° =>a+b+c+d+e=180° Hence proved By Anuj Acharjee(India)class-7
@pradeepabk
4 жыл бұрын
1. Exterior angle of any regular polygon is 360/n, where n is the number of sides of that polygon. 2. So here it is pentagon, so exterior angle is 72. 3. There are 5 identical triangles formed, and all of them with two angles as 72, then third angle must be 36 (= 180-72-72) 4. Now 36 * 5 = a+b+c+d+e = 180 degrees. If in case polygon is not identical, then also, sum of interior angles of polygon is 180(n-2) = 540. sum of exterior angles = 360 . (simply clockwise) sum of another set of exterior angles = 360 (simply anti-clockwise) sum of all triangles formed outside polygon = 5 *180 =900. Now we know that a+b+c+d+e + 360 + 360 =900 gives a+b+c+d+e+f = 180 degrees
@abhishekshrivastava6963
3 жыл бұрын
LOL I did this in 10 sec I AM from India and this year I am at 9th you just have to take that small triangle in which angle A is their and now If you find out by exterior angle property By dividing figure into 2 triangles ,angles of triangle with ANGLE A will be like this angle A angle E +angle C angle B+angle D SO,answer will be ANGLE(A+E+C+B+D)=180 degrees(coz all angles of a triangle sum to 180degree) BTW I haven't watched full video I am commenting just after solving question
@Who_raviverma
3 жыл бұрын
So basically i have an easy one, First we need to consider inner Pentagon, so angle of vertex of Pentagon is 72°. So then we can take any triangle of the star, and then we know sum of angles of all 3 angle of triangle is 180°. So, as these triangles are isosceless ,Suppose we get X +2Y=180°------(1). X Is the angle we need to find (Dark blue coloured) and Y is the base angle. So Now Fo Y we can write Y=180°-72°=108° so now in equation (1) we get X=36°. So all traingles are Congruent so sum of all is 36×5= 180°. 🤪🤪Damn that is a big comment
@priyansh_12391
Жыл бұрын
Never let them know your next move: Pulls up a protractor
@AryanKumar-jo1pz
3 жыл бұрын
Angle sum of Pentagon= (n-2)*180 = 540 degrees so assuming the pentagon in the centre is regular, anyone interior angle = 540/5 =108 using angle sum property of a straight line, any exterior angle = 180-108 = 72 consider the smallest triangle with any one angle. angle sum of a triangle = 180 therefore, angle a + 72 + 72 = 180 that gives, a = 36 all angles are equal so a = 36*5 = 180 Nice quesiton PS: WOW! That 1st trick is so interesting
@HarshitKumar-jj3td
3 жыл бұрын
Solve : If a^2 + (1/a^2)+b^2+(1/b^2)+ c^2+(1/c^2) = 0, find the value of a, b and c. This question was asked in SOF olympiad of maths for 15 years olds. My name is Harshit Kumar Singh.
@the.aayushya
4 жыл бұрын
We can prove that the total area of the pentagon is 540 by dividing it into a triangle and a trapezium. Then each angle of the trapezium is equal to 108°. Then the equal angles of the 5 isosceles triangles are equal to 72°( linear pair). a = 180°-2×72° = 36° We know that a=b=c=d=e So 5a = 180° This was a simple problem.
@mystifiedgamer2632
3 жыл бұрын
Quite easy as I did some construction, use the property of alternate interior angles and use the angle sum property of the triangle. And we get our answer as 180°
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