Answer:
(c) 36°
Step-by-step explanation:
We assume the pentagon is regular, so each central angle is congruent to the others. Each central angle is bisected by an apothem.
Angle 1
Angle 1 is one of 5 congruent central angles, so its measure is ...
∠1 = 360°/5 = 72°
Angle 2
Angle 2 is the result of one of the isosceles triangles having its central angle being bisected by an altitude. Its measure is half that of angle 1:
∠2 = 72°/2 = 36°
The measure of angle 2 is 36°.
Angle 3
Angle 3 is the other acute angle in the right triangle in which angle 2 is one of the acute angles. Its measure is ...
∠3 = 90° -∠2 = 90° -36° = 54°
