Question

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

Answer 1

$\angle BAD={120}^{\circ }and\angle DBC=x$
$\angle B=2\times \angle DBC=2x$
[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 ${30}^{\circ }$.