Question

In the given figure, AB||CD then the value of x is

• A. ${285}^{\circ }$
• B. ${75}^{\circ }$
• C. ${235}^{\circ }$
• D. ${220}^{\circ }$

Answer 1

The correct option is A ${285}^{\circ }$

$\angle 1={45}^{\circ }$ [Alternate angles]
$\angle 2={30}^{\circ }$ [Alternate angles]
$\angle BOC=\angle 1+\angle 2$
$\angle BOC={45}^{\circ }+{30}^{\circ }={75}^{\circ }$
$\text{So,}x={360}^{\circ }-\angle BOC={360}^{\circ }-{75}^{\circ }={285}^{\circ }$
$\text{Hence,}x={285}^{\circ }.$