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angles wanted, isosceles trapezoid, inside a square, <BAP=30^o, <BCP=15^o

Source: 2016 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p11

April 27, 2021
geometrytrapezoidsquareanglesUkraine Correspondence

Problem Statement

Inside the square ABCDABCD mark the point PP, for which ∠BAP=30o\angle BAP = 30^o and ∠BCP=15o\angle BCP = 15^o. The point QQ was chosen so that APCQAPCQ is an isosceles trapezoid (PC∥AQPC\parallel AQ). Find the angles of the triangle CAMCAM, where MM is the midpoint of PQPQ.
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