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

9514 1404 393

  ∠5 = 60°

  ∠6 = 30°

  ∠7 = 120°

Step-by-step 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°

2 5/8 is the final answer! : )