In ∆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?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 55°.
∠APB = 90 + ∠C/2
∠APB = 90 + 70/2 = 90 + 35 = 125
∠APB + ∠DPB = 180 (Straight line)
125 + ∠BPD = 180
∠BPD = 180 – 125 = 55