Question

What is the sum of the exterior angles of a convex polygon?

A. 360

B. 180(n – 2)

C. 180

D. 360n

Answer 1

A

Explanation:

The sum of the exterior angles for each polygon is always 360°.

The sum of the interior angles for each polygon is always 180°(n-2).

If you have n-sided convex polygon, then

`\left(\text{Sum of all interior angles}\right)+ \left(\text{ Sum of all exterior angles}\right)=180^(\circ)\cdot n`

So,

`\left(\text{Sum of all interior angles}\right)+ 180^(\circ)\cdot (n-2)=180^(\circ)\cdot n\\ \\\left(\text{Sum of all interior angles}\right)=180^(\circ)\cdot n-180^(\circ)\cdot (n-2)=180^(\circ)\cdot (n-n+2)=360^(\circ)`