Question

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

Answer 1

$PQ\parallel ST,\angle PQR={110}^{\circ }$ and $\angle RST={130}^{\circ }$

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

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

$\Rightarrow {110}^{\circ }+\angle QRX={180}^{\circ }$

$\Rightarrow \angle QRX={70}^{\circ }$

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

${130}^{\circ }°+\angle SRY={180}^{\circ }$

$\angle SRY={50}^{\circ }$

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

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

$\therefore \angle QRS={60}^{\circ }$