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  • 4 years ago

What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 72°?

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  1. Directrix
    • 4 years ago
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    The sum of the exterior angles, one per vertex, of a regular polygon is 360. If one exterior angle is 72, then the number of sides of the polygon is 360/72 = 5. The regular polygon is a regular pentagon. If the exterior angle measures 72, its adjacent interior angle is 180 - 72 = 108. The sum of the interior angles is 108 times 5 = 540 degrees.

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