Question

Find the value of $x$ in the following figure in order to make $AB\parallel CD$.

• A. ${31}^{\circ }$
• B. ${11}^{\circ }$
• C. ${21}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is C ${21}^{\circ }$

If $AB\parallel CD$, then $\angle MPB$ and $\angle PQD$ should be equal as they would be corresponding angles.

Hence,
$\angle MPB=\angle PQD$
$\Rightarrow (4x-31{)}^{\circ }=(3x-10{)}^{\circ }\Rightarrow 4x-3x={31}^{\circ }-{10}^{\circ }\Rightarrow x={21}^{\circ }$

So, the value of $x$ should be ${21}^{\circ }$ so that AB and CD becomes parallel.