Geometry Problem on Finding Angles

Question

In an isosceles triangle ABC,AB=AC,P and Q are points on AC and AB respectively such that CB=BP=PQ=QA.Then prove that angle AQP=900/7

Answer 1

Hints: Make a drawing, then

$$\alpha:=\angle BCP=\angle ABC\;,\;\;\angle PBC=180^\circ-2\alpha\implies \angle QBP=3\alpha-180^\circ=\angle PQB\implies$$

$$\implies \angle AQP=360^\circ-3\alpha$$