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  4. In the given figure, ABCDE is a pentagon, inscribed in a circle with centre prime O prime. CD = DE and AD = BD . angle EAD =40°, angle BOC =90°. Then, the value of angle ADE is

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Q. In the given figure, $ABCDE$ is a pentagon, inscribed in a circle with centre ${ }^{\prime} O ^{\prime}$. $CD =$ $DE$ and $AD = BD . \angle EAD =40^{\circ}, \angle BOC =90^{\circ}$. Then, the value of $\angle ADE$ is____Mathematics Question Image

Geometry

Solution:

Since $A D=B D$ and $C D=D E$,
$AE = BC \Rightarrow \angle BOC =\angle AOE =90^{\circ} $
$\Rightarrow \angle ADE =(\frac{1}{2}) \angle AOE =(\frac{1}{2}) 90^{\circ}=45^{\circ}$