Question

prove that the sum of all exterior angles formed by producing the sides of a convex polygon in the same order is equal to four right angles.

Answer 1

If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is

360° .

Consider the sum of the measures of the exterior angles for an

n -gon.

The sum of the measures of the exterior angles is the difference between the sum of measures of the linear pairs and the sum of measures of the interior angles.

That is, the sum of the exterior angles

n is

N=180n−180(n−2)

Distribute

180

N=180n−180n+360      =360