Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\angle BAD={120}^{\circ }and\angle DBC=x$
$\angle B=2\times \angle DBC=2x$ [Since, diagonals bisect the angles in rhombus]
We have,
$\angle DAB+\angle B={180}^{\circ }$ [sum of adjacent angles of rhombus are equal to ${180}^{\circ }$]
$\Rightarrow {120}^{\circ }+2x={180}^{\circ }$
$\Rightarrow 2x={180}^{\circ }-{120}^{\circ }$
$\Rightarrow x=\frac{60}{2}={30}^{\circ }$
Hence, the value of 'x' is ${30}^{\circ }$ .