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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