Question

Given the regular decagon, what is the measure of each numbered angle? A. m∡1 = 72°; m∡2 = 18°; m∡3 = 36° B. m∡1 = 18°; m∡2 = 36°; m∡3 = 72° C. m∡1 = 36°; m∡2 = 72°; m∡3 = 18° D. m∡1 = 36°; m∡2 = 18°; m∡3 = 72°

Answer 1

D is the answer I think

Answer 2

D. m∡1 = 36°; m∡2 = 18°; m∡3 = 72°

Explanation:

The 10 central angles are all the same for the regular decagon, so each is 1/10 of 360°. Angle 1 is 36°.

Angle 2 is half of angle 1, since the altitude shown is an angle bisector. Angle 2 is 18°.

Angle 3 is the complement of angle 2. It is the other acute angle in the triangle that has angle 2 marked. Angle 3 is 72°.