If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary:
[tex]85+C=180[/tex][tex]C=180-85=95[/tex]
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°
