In triangle $XYZ$, $\angle XYZ = \angle YXZ$ and $\angle XYZ = 70^\circ$. If $\overline{YW}$ is extended to point $P$ such that $\angle YWP$ is an exterior angle of $\triangle XYZ$, what is the measure of $\angle YWP$? Let's think step by step and output the final answer within \boxed{}.
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