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Find the Angles

Source: Israel Autumn 2016 TST2/1

September 29, 2016
geometrytrapezoid

Problem Statement

A square ABCDABCD is given. A point PP is chosen inside the triangle ABCABC such that ∠CAP=15∘=∠BCP\angle CAP = 15^\circ = \angle BCP. A point QQ is chosen such that APCQAPCQ is an isosceles trapezoid: PC∥AQPC \parallel AQ, and AP=CQ,AP∦CQAP=CQ, AP\nparallel CQ. Denote by NN the midpoint of PQPQ. Find the angles of the triangle CANCAN.
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