Question

If each interior angle of a regular polygon is 4 times its exterior angle then the number of diagnoals is

Answer 1

the exterior angle = 180 / 5 = 36 degrees. you get interior angle = 4 * exterior angle = 4 * 36 = 144 degrees. 144 + 36 = 180 degrees so they are supplementary as required. the exterior angle of the regular polygon is equal to 360 / number of sides.