Question

In the given figure, what is the value of $x$ ?

• A. ${30}^{\circ }$
• B. ${20}^{\circ }$
• C. ${15}^{\circ }$
• D. ${10}^{\circ }$

Answer 1

The correct option is B ${20}^{\circ }$

Consider the cyclic quadrilateral ABDE.
Since opposite angles are supplementary in a cyclic quadrilateral,
$\angle AED+\angle DBA={180}^{\circ }.$
$⟹\angle DBA={180}^{\circ }-{110}^{\circ }={70}^{\circ }$

Now, $\angle ABD+\angle DBC={180}^{\circ }.\left(\text{Linear pair}\right)$

$⟹\angle DBC={180}^{\circ }-{70}^{\circ }={110}^{\circ }$

Now, consider $△DBC.$

We know that the sum of all the angles of a triangle is always ${180}^{\circ }.$

i.e., $\angle DBC+\angle BCD+\angle CDB={180}^{\circ }$

$⟹\angle CDB={180}^{\circ }-({110}^{\circ }+{50}^{\circ })={20}^{\circ }$
Thus, $x={20}^{\circ }.$