Question

In Figure, if $PQ\parallel ST,\angle PQR={110}^o$ and $\angle RST={130}^o$, find $\angle QRS$.

• A. ${90}^o$
• B. ${60}^o$
• C. ${30}^o$
• D. ${45}^o$

Answer 1

The correct option is B ${60}^o$

Given :$PQ||ST$, $\angle PQR={110}^o$ and $\angle RST={130}^o$

Construction: A line $XY$ parallel to $PQ$ and $ST$ is drawn.

$\angle PQR+\angle QRX={180}^o$ (Angles on the same side of transversal.)

${110}^o+\angle QRX={180}^o$

$\angle QRX={180}^o-{110}^o$

$\angle QRX={70}^o$

Also,$\angle RST+\angle SRY={180}^o$ (Angles on the same side of transversal.)

${130}^o+\angle SRY={180}^o$

$\angle SRY={50}^o$

Now,$\angle QRX+\angle SRY+\angle QRS={180}^o$

${70}^o+{50}^o+\angle QRS={180}^o$

$\angle QRS={60}^o$

Hence, $\angle QRS={60}^o$