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 ${360}^{\circ }$.
$\angle C$ = ${75}^{\circ }$
We know that the interior angle and exterior angle are supplementary for the vertices of a polygon.
Interior angles:
$\angle BAC={180}^{\circ }-{55}^{\circ }={125}^{\circ }$
$\angle ABD={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$\angle A+\angle B+\angle C+\angle D={360}^{\circ }$
$\angle D={360}^{\circ }-(\angle A+\angle B+\angle C)$
= ${360}^{\circ }-({125}^{\circ }+{120}^{\circ }+{75}^{\circ })$
= ${360}^{\circ }-{320}^{\circ }$
= ${40}^{\circ }$

Since, $\angle D$ and $\angle x$ are vertically opposite angles,
$\angle D=x^{\circ }$
So, $x={40}^{\circ }$