In isosceles triangle ABC, ∠A = 80°. The bisectors of the base angles, ∠B and ∠C, intersect at point P.

Question

∠BPC =

Answer 1

I made my sketch so that angle B = angle C = 50°

So the bisected angles are 25° each
and angle BPC = 180 - 25 - 25 = 130°

Answer 2

this looks like some hard triganomitry

Answer 3

Not trigonometry involved here.
It is elementary geometry, based on the definition of an isosceles triangle, and the fact that the angles in any triangle add up to 180°