Why do the interior Angles of a 5 point star always equal 180 degrees?

Answer 1

Funny thing is, I was just asked to do this in my geometry class. And I figured out this method that my teacher had never heard of. Ok, let's say that the five angles are named angles A, B , C, D, and E, going aound counter clockwise. Points ACD form a trinalge, and everybody knows that a triangle forms 180 degrees. But, i problem, you are missing two angles that would complete the triangle. While thinking on this problem last week in my 9th grade geometry class, I realized that the sum of the two missing angles is equivilant to the sum of angles B and E, the two "left over" angles, unused in the triangle. Thus, the sum of all five angles MUST add up to 180 degrees. I went a little farther to figure out why exactly the sum of the two "missing" angles is equal to the sum of angles B and E all the time, no matter how you manipulate it. Let's call the point formed going in towards the center of the triangle formed by angles C and D point F. There are two triangles formed here, triangle FCD and triangle BEF. The foint shared creates two vertical angles, meaning they are equal. Then the "left over" amount of degrees in both triangles has to be the same, proving that the sum of the two missing angles will be equal to the sum of angles B and E. There you go,, PLEASE do not copy this to use on a project. I will hear abput it and just, ...............................................