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<PCA=? <PAB = 30^o, <PBA = 20^o in 100-40-40 triangle

Source: Netherlands - Dutch NMO 1973 p3

January 27, 2023
anglesgeometryisosceles

Problem Statement

The angles AA and BB of base of the isosceles triangle ABCABC are equal to 40o40^o. Inside △ABC\vartriangle ABC, PP is such that ∠PAB=30o\angle PAB = 30^o and ∠PBA=20o\angle PBA = 20^o. Calculate, without table, ∠PCA\angle PCA.
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