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°.

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

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