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Full video (sum of angles in star general case)

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Inside angles of a pentagon are 540, 108 per angle, so both angles of the triangle attached to the pentagon are 72.
180-(72×2)=36. 36x5=180.

madhatterhillbilly

Same method can be used for a triangle, square, hexagon, etc.

randyconn

e+c+top right of pentagon = 180. Same for b and d triangle. Angles on straight line are also 180. So a+(b+d)+(c+e) = top triangle =180

shrankai

I did it by exterior angle property,
as b+d will be equal to the angle on left side of triangle 'a'
and similarly e+c will be equal to angle on lower right of triangle "a'
therefore sum of all angles in triangle will be 180
a+b+c+d+e=180

quanta

The same question was given as a practice problem in geometry when I was in 6th grade. By simple geometry we can easily find that the sum is 180°. This visual representation is nice and can be understood easily 👍

tigerinthejungle_

I love it when Presh gets in on a debate. Good job, bro, sticking up for that other channel.

BKNeifert

Pentagon has 540 degrees, meaning each angle inside is 108. Subtract 108 from 180 to get 72 degrees, the measure of the 2 equal angles in each triangle. 180 degrees in a triangle, minus 72, minus 72, gets you the 3rd angle of the triangle, 36. There are 5 of these angles, so 36x5 equals 180

aidanonbrawl

each bllue angle will be half of a exterior angle of the pentagon (imagining as a part of circle) and some of exterior angles will be 360 hence the answer is 360/2=180 degrees

sanskardutt

Answer: 180.
Assuming this is a regular pentagon, each angle is 180(5-2)/5=540/5=108. Because a straight line is 180°, the innermost angles of each outer triangle is 180-108=72. The triangle must sum to 180. 72*2=144, then 180-144=36. Since there are 5 of these, 36*5=180.

PopeVancis

The blue arrows were turning 36 degrease every turn which sums up to 180

Cringeshorts

The star is inscribed into a circle, vertices of the star divide the 2pi circle into 2pi / n equal arcs, where n is the number of vertices. Each of the angles opposes an arc, so each angle is pi/n, and the sum is n * pi / n = pi
Works for non-symmetrical (but inscribed) stars too =)

iliapahalko

I got it from the fact that the total angles of an n-gon is (n-2)π radians. Then the pentagon inside has (5-2)π / 5 per inner vertex = 3/5 π. After that, you see that the triangle at the points is isoceles and that it has 2 angles that are the same (lets called them β). We see that β forms π rad or 180° with the 3/5 π angle. Then β =π - 3/5 π = 2/5 π. And from the triangle at the point follows that α + 2β = π (α the angle at the points). Thus α = π - 2*(2/5) = π/5. And that means all five cornes make an angle sum of (π/5)*5 = π rad= 180°.

drkorp-