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22 October, 00:10

Find the measure of each interior angle AND each exterior angles of the following regular polygons. Show your work.

a. Pentagon

b. 16-gon

c. Dodecagon

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Answers (1)
  1. 22 October, 03:29
    0
    Given

    regular polygons with 5, 16, and 12 sides

    Find

    the measures of each interior and exterior angle

    Solution

    The sum of exterior angles is 360° for any convex polygon. For a regular n-agon, the measure of an exterior angle is 360°/n. The corresponding interior angle is its supplement.

    (a) pentagon. Exterior angle: 72°; Interior angle: 108°.

    (b) 16-gon. Exterior angle: 22.5°; Interior angle: 157.5°.

    (c) dodecagon. Exterior angle: 30°; Interior angle: 150°.
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