SOLUTION: Starting from the sum of exterior angles prove that in a regular polygon of n sides, the measure of each interior angle is n-2*180/n.
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-> SOLUTION: Starting from the sum of exterior angles prove that in a regular polygon of n sides, the measure of each interior angle is n-2*180/n.
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Question 632406: Starting from the sum of exterior angles prove that in a regular polygon of n sides, the measure of each interior angle is n-2*180/n. Answer by solver91311(24713) (Show Source):
The sum of the exterior angles of a convex polygon of any number of sides is . Hence the measure of any individual exterior angle of a regular -gon is . From the definition of an exterior angle of a polygon we know that the terminal ray of the exterior angle (the ray that is not the side of the polygon) forms a straight angle with an adjacent side of the polygon. Hence it can be seen that the exterior angle and the adjacent interior angle are supplementary. Hence the measure of the adjacent interior angle is given by:
The rest is just a little algebra that you can handle yourself.
John
My calculator said it, I believe it, that settles it
