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The regular polygon has radii and an apothem as shown. Find the measure of each numbered angle.

The regular polygon has radii and an apothem as shown. Find the measure of each numbered-example-1
User Nick Coons
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9514 1404 393

Answer:

∠5 = 60°

∠6 = 30°

∠7 = 120°

Explanation:

Since the polygon is regular, you know that the central angle (7) is 1/3 of the circle, or 120°. The angle 5 is half that measure, so is 60°, and the angle 6 is the complement of angle 5, so is 30°. (Angle 6 is also half the inscribed angle at each vertex, said inscribed angle being 120°/2 = 60°.)

∠5 = 60°

∠6 = 30°

∠7 = 120°

User Yangguang
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