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find the value of an angles

Source: 1st National Women´s Contest of Mexican Mathematics Olympiad 2022, problem 2 teams

July 23, 2023
geometryisoscelesMexicoangles

Problem Statement

Consider △ABC\triangle ABC an isosceles triangle such that AB=BCAB = BC. Let PP be a point satisfying
∠ABP=80∘,∠CBP=20∘,andAC=BP\angle ABP = 80^\circ, \angle CBP = 20^\circ, \textrm{and} \hspace{0.17cm} AC = BP
Find all possible values of ∠BCP\angle BCP.
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