Question

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

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$

Sum of all the interior angles in a quadrilateral is ${360}^{\circ }$.
$\angle D$ = ${75}^{\circ }$
We know that the interior angle and exterior angle are supplementary for the vertices of a polygon.
Interior angles:
$\angle BAD={180}^{\circ }-{55}^{\circ }={125}^{\circ }$
$\angle ABC={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

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

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