Question

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

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

Answer 1

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

$\angle 1={45}^{\circ }$ [Alternate to $\angle$ABO]
$\angle 2={30}^{\circ }$ [Alternate to $\angle$DCO]
$\angle BOC=\angle 1+\angle 2$
$\angle BOC={45}^{\circ }+{30}^{\circ }={75}^{\circ }$

[Angles about a point = ${360}^{\circ }$]
So, $x=360-\angle BOC$
$=360-75={285}^{\circ }$