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Question

In the given figure, AC is a diameter of the circle. Find the value of x.

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Solution

Since angle in a semicircle is a right angle, we have
ABC=90.
But, ABD+DBC=ABC
i.e., ABD+36=90
ABD=54
Consider the cyclic quadrilateral ABDE. Since opposite angles are supplementary, we have
ABD+x=180
x=18054=126

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