Question

A quadrilateral is inscribed in a circle. Find the measure of each missing angle as labeled below. explain answer please

Answer 1

9514 1404 393

Answer:

• C = 95°
• D = 72°
• F = 108°

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°