Question

In the figure given below,
ABCD is a rhombus. Find the value of x.

• A. ${20}^{\circ }$
• B. ${25}^{\circ }$
• C. ${30}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is B ${25}^{\circ }$


We know that a rhombus is a parallelogram and the adjacent angles of a parallelogram are supplementary.

$\text{Hence,}\angle A+\angle B={180}^{\circ }$
${130}^{\circ }+\angle ABD+\angle DBC={180}^{\circ }...\left(i\right)$

We also know that diagonals of a rhombus bisect its angles.

Therefore,
$\angle ABD=\angle DBC=x$

Now, from equation (i)
${130}^{\circ }+x+x={180}^{\circ }$
$2x={180}^{\circ }-{130}^{\circ }$
$2x={50}^{\circ }$
$x=\frac{{50}^{\circ }}{2}$
$x={25}^{\circ }$
$\text{Hence, the value of}x=25°.$