Question

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

• A. ${50}^{\circ }$
• B. ${40}^{\circ }$
• C. ${30}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$


In rhombus ABCD, all sides are equal.
Considering $\Delta ADC$;
As $AD=DC\Rightarrow \angle DAC=\angle DCA={40}^{\circ }$
So in triangle DOC,
$\angle CDO=y$
$\angle DCO={40}^{\circ }$
As exterior angle of a triangle is equal to the sum of interior angles.
$\Rightarrow y+\angle DCO=\angle COB$
$y+40=x$
$x-y={40}^{\circ }$
So, the correct answer is option (b).