Question

Complete this statement: The sum of the measures of the exterior angles of an n-gon, one at each vertex, is _____ degrees.

a) 360
b) (n-2)180
c) $\frac{(n-2)180}{n}$
d) 180n

Please help ASAP.

Answer 1

Answer: option a. 360 °.

Explanation:

The exterior angles of simple polygons add up 360°.

That is so because making the route of the exterior angles one by one takes you to make a complete revolution (turn), which as we know is 360 °.

You can see that if you draw any polygon and mark its exterior angles and translate all the segments (keeping the angles) to a common vertex. There you will see the angles cover all the circle, so the sum of the angles is 360°.