In Δ ABC, ∠C = 70°. The bisectors of ∠A and<B meet BC and AC in points D and E, respectively. AD and BE intersect each other at P. What is the measure of ∠DPB?
55°
The correct answer is 55°.
The angle formed at the incenter by two angle bisectors (e.g., $\angle APB$) is related to the third angle of the triangle ($\angle C$) by the formula $\angle APB = 90^\circ + \angle C/2$. Similarly, $\angle BPC = 90^\circ + \angle A/2$ and $\angle CPA = 90^\circ + \angle B/2$. Understanding these properties is crucial for solving problems involving angle bisectors and the incenter in triangle geometry.
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