Find the sum of the measures of the exterior angles of a convex octagon.

A) 180 degrees

B) 360 degrees

C) 720 degrees

D) 1080 degrees

E) 1440 degrees

B) 360 degrees

Explanation:

In any convex polygon, the sum of the exterior angles will be 360°.

We can text this for the octagon, assuming a regular octagon where all angles and sides are equal.

One of the exterior angles is calculated by subtracting the interior angle from 180°. Find the measure of one interior angle, then subtract it from 180° to find one exterior angle. Then multiply the exterior angles by 8 to find the sum of all exterior angles.

The sum of the interior angles is calculated by 180° times the number of sides (n) subtract 2. An octagon has 8 sides, so n = 8.

180° (n - 2) Substitute (replace) n with 8

= 180° (8 - 2) Subtract inside the brackets

= 180° (6) Multiply

= 1080° Sum of all interior angles

Since every angle is the same and there are 8 angles, divide the sum of all interior angles by 8.

1080° : 8 = 135°

One interior angle is 135°. Its corresponding exterior angle is calculated by subtracting from 180°.

180° - 135° = 45°

Multiply one exterior angle by 8 because there are 8 exterior angles.

45° X 8 = 360°

Therefore, you can prove the sum of all the measures of the exterior angles of a convex octagon is 360°.