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7 June, 19:30

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

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  1. 7 June, 19:49
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    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°.
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