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.m

Answer 1

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary:

$85+C=180$$C=180-85=95$

So, m∠C=95

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

D = 144°/2 = 72°

F = 180° -D = 180° -72° = 108°

And CDE=95+72+85=252°