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Question

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


A
100
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B
126
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C
136
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D
154
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Solution

The correct option is B 126
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

Mathematics

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