Question

In the given figure, if AB || CD, then find the value of x.

​

• A. ${235}^{\circ }$
• B. ${275}^{\circ }$
• C. ${220}^{\circ }$
• D. ${285}^{\circ }$

Answer 1

The correct option is D

${285}^{\circ }$

Construction: Draw a line P passing through O and parallel to AB and CD.

$\angle 1={45}^{\circ }$ [Alternate interior angles are equal]
$\angle 2={30}^{\circ }$ [Alternate interior angles are equal]

$\angle BOC=\angle 1+\angle 2$
$\Rightarrow \angle BOC={45}^{\circ }+{30}^{\circ }={75}^{\circ }$

Angle around a point is 360°.
So, $x+\angle BOC=360°$
$\Rightarrow x$ = 360° - $\angle$BOC
$\Rightarrow x$ = 360° - 75° = 285°

Hence, the value of x is 285°.