Question

In the given figure, ABCD is a rhombus, then the value of ′𝑥′ is:​

• A. ${90}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

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


$\angle BAD={120}^{\circ }$ and $\angle DBC=x$
$\angle B=2\angle DBC=2x$
[ Since the diagonals bisects the angles in rhombus]

We have,
$\angle DAB+\angle ABC={180}^{\circ }$
[Co-interior angles in the same side of transversal]

Now,
$\Rightarrow {120}^{\circ }+2x={180}^{\circ }$
$\Rightarrow 2x={180}^{\circ }-{120}^{\circ }$
$\Rightarrow 2x={60}^{\circ }$
$\Rightarrow x={30}^{\circ }$

Hence the value of $x={30}^{\circ }$