Question

In the given figure, find the value of 'x'.

• A. 30
• B. 40
• C. 50
• D. 60

Answer 1

The correct option is B

40

Sum of all the interior angles in a quadrilateral is ${360}^{\circ }$
$\angle C$ = ${75}^{\circ }$

Let's find the other interior angles.
We know that the interior angle and exterior angle are supplementary for the vertices of a polygon.
Interior angles: $\angle A$ = ${180}^{\circ }$ - ${55}^{\circ }$ = ${125}^{\circ }$
$\angle B$ = ${180}^{\circ }$ - ${60}^{\circ }$ = ${120}^{\circ }$

$\angle A$ + $\angle B$ + $\angle C$ + $\angle D$ = ${360}^{\circ }$
$\angle D$ = ${360}^{\circ }$ - ($\angle A$ + $\angle B$ + $\angle C$)
= ${360}^{\circ }$ - (${125}^{\circ }$ + ${120}^{\circ }$ + ${75}^{\circ }$)
= ${360}^{\circ }$ - ${320}^{\circ }$
= ${40}^{\circ }$
Since, $\angle D$ and x are vertically opposite angles
$\angle D$ = x${}^{\circ }$;
So, x = 40