Question

A quadrilateral is inscribed in a circle. Find the measure of each missing angle as labeled below. Show your work and/or explain how you got your answer.

1 point for each correct angle measure and 1 point for explaining or showing how you got your answer. Don’t forget to label your answers.

Answer 1

C = 95°

D = 72°

F = 108°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary. Inscribed angles are half the measure of the arc they subtend. (The latter statement can be used to prove the former one.)

Using these relations, we have .

C = 180° -E = 180° -85° = 95°

D = 144°/2 = 72°

F = 180° -D = 180° -72° = 108°