Question

Each regular polygon has radil and apothem as shown. Find the measure of each numbered angle. ​

Answer 1

Answer:

∠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°