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Tuymaada 1999, Q5

Source: Tuymaada 1999, Q5

July 31, 2012
geometrygeometric transformationreflectiontrigonometrygeometry unsolved

Problem Statement

In the triangle ABCABC we have ∠ABC=100∘\angle ABC=100^\circ, ∠ACB=65∘\angle ACB=65^\circ, M∈ABM\in AB, N∈ACN\in AC, and ∠MCB=55∘\angle MCB=55^\circ, ∠NBC=80∘\angle NBC=80^\circ. Find ∠NMC\angle NMC.
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