Question

In the given figure, if 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 ${285}^{\circ }$

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


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

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

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

Hence the value of x is 285°.