Question

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

Answer 1

Since angle in a semicircle is a right angle, we have
$\angle ABC={90}^{\circ }.$
But, $\angle ABD+\angle DBC=\angle ABC$
i.e., $\angle ABD+{36}^{\circ }={90}^{\circ }$
$⟹\angle ABD={54}^{\circ }$
Consider the cyclic quadrilateral ABDE. Since opposite angles are supplementary, we have
$\angle ABD+x={180}^{\circ }$
$⟹x={180}^{\circ }–{54}^{\circ }={126}^{\circ }$