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

∠BPC =

3 answers

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°
this looks like some hard triganomitry
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°