Question

In the given figure, ABCD is a rhombus, then the value of 'x' is

• A. ${45}^{\circ }$
• B. ${50}^{\circ }$
• C. ${30}^{\circ }$
• D. ${65}^{\circ }$

Answer 1

The correct option is C ${30}^{\circ }$


Given:
$\angle BAD={120}^{\circ }and\angle DBC=x$
$\angle B=2\angle DBC=2x$ [Since, diagonals bisect the angles in rhombus]
We have,
$\angle DAB+\angle ABC={180}^{\circ }$ [Co-interior angles on the same side of transversal]
$\Rightarrow {120}^{\circ }+2x={180}^{\circ }$
$\Rightarrow 2x={180}^{\circ }-{120}^{\circ }$
$\Rightarrow x=\frac{60}{2}={30}^{\circ }$
Hence, the value of $x$ is ${30}^{\circ }$ .