HMMT 2010 G9

Geometry
Answer

Let $A B C D$ be a quadrilateral with an inscribed circle centered at $I$ . Let $C I$ intersect $A B$ at $E$ . If $\angle I D E=35^{\circ}, \angle A B C=70^{\circ}$ , and $\angle B C D=60^{\circ}$ , then what are all possible measures of $\angle C D A$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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70^{\circ} \text{ and } 160^{\circ}

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