Question

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

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

Answer 1

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

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