Question

If $AB\parallel CD$, find the value of $x$ in the following figure.

• A. ${25}^{\circ }$
• B. ${20}^{\circ }$
• C. ${30}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is B ${20}^{\circ }$

AB and CD are parallel.
Therefore,
$(5x-10{)}^{\circ }+(3x+30{)}^{\circ }={180}^{\circ }$ [Sum of the interior angles on the same side of a transversal is ${180}^{\circ }$]

$\Rightarrow 5x-{10}^{\circ }+3x+{30}^{\circ }={180}^{\circ }$
$\Rightarrow 8x+{20}^{\circ }={180}^{\circ }$
$\Rightarrow 8x={180}^{\circ }-{20}^{\circ }$
$\Rightarrow 8x={160}^{\circ }$
$\Rightarrow x=\frac{{160}^{\circ }}{8}$
$\Rightarrow x={20}^{\circ }$

Hence, the value of $x$ is ${20}^{\circ }$.