Mock AIME 1 2006-2007 Problems/Problem 8

Problem

Let $ABCDE$ be a convex pentagon with $AB\sqrt{2}=BC=CD=DE$ , $\angle ABC=150^\circ$ , $\angle BCD=75^\circ$ , and $\angle CDE=165^\circ$ . If $\angle ABE=\frac{m}{n}^\circ$ where $m$ and $n$ are relatively prime positive integers, find $m+n$ .

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Mock AIME 1 2006-2007

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Mock AIME 1 2006-2007 Problems/Problem 8

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