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Question 8

In the adjoining figure, $$AD=AE$$. The measure of $$\angle EAD$$ is
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Solution

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In right triangle $$ABC$$, the other angles are $$2x$$ and $$\frac{x}{2}$$. Thus $$2x+\frac{x}{2}=90^\circ$$, giving $$x=36^\circ$$. Since $$AD=AE$$, the base angles of triangle $$ADE$$ are both $$36^\circ$$, so $$\angle EAD=180^\circ-72^\circ=108^\circ$$.

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