# What a triangle is that?

Geometry Level 4

Given a triangle $$ABC$$ with $$\measuredangle ACB=100$$ and $$\measuredangle BAC=30$$, point $$M$$ lies on the side $$AC$$,such that $$CM=CB$$. If the ratio $$BM:AC=p:q$$, where $$p$$ and $$q$$ are co-prime positive integers, compute $$p+q$$ .

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