Question

If $RS\parallel PQ$ and $RT\parallel UQ$, then find the value of $8x-2y$.

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${150}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

Since, $RT\parallel UQ$ and $QR$ is a transversal.
$\angle UQR=\angle QRT$ (Alternate angles)
$\Rightarrow y={90}^{\circ }$
Also, $\angle PQU+{150}^{\circ }={180}^{\circ }$ (Linear pair)
$\Rightarrow \angle PQU={180}^{\circ }-{150}^{\circ }={30}^{\circ }$
And $PQ\parallel RS$ and $RQ$ is transversal.
$\angle PQS=\angle QRS$ (Alternate angles)
$\Rightarrow \angle PQU+\angle UQR=\angle SRT+\angle TRQ$
$\Rightarrow {30}^{\circ }+{90}^{\circ }=x+{90}^{\circ }\Rightarrow x={30}^{\circ }$
Now, $8x-2y=8\times {30}^{\circ }-2\times {90}^{\circ }$
$={240}^{\circ }-{180}^{\circ }={60}^{\circ }$.