Question

In the given diagram, ABCD is a rhombus.

What is the value of (x – y)?

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

Answer 1

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


$x={90}^{\circ }$
($\because$ Diagonals of rhombus bisect each other at right angles.)

Now, in $\Delta ADC,$
$AD=DC$ (Sides of rhombus)
$\therefore \angle DAC=\angle ACD={40}^{\circ }$
($\because$ Equal sides have equal angles opposite to them.)

Now in $\Delta OCD,$
$\angle DOC={90}^{\circ }$
($\because$ angles of a rhombus bisect at right angles)
$y={180}^{\circ }-({90}^{\circ }+{40}^{\circ })$
$\Rightarrow y={180}^{\circ }-{130}^{\circ }={50}^{\circ }$

$\therefore x-y={90}^{\circ }-{50}^{\circ }={40}^{\circ }$