Answer:
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°.
