Question

If $PQ||ST,\angle PQR={110}^o$ and $\angle RST={130}^o$, find $\angle QRS\left(Indegrees\right)$

Answer 1

Draw a line XY parallel to $PQ\parallel ST$.

It is known that the sum of interior angles on the same side of the transversal is ${180}^{\circ }$. So,

$\angle PQR+\angle QRX={180}^{\circ }$

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

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

Similarly,

$\angle RST+\angle SRY={180}^{\circ }$

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

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

Now, by property of linear pair,

$\angle QRX+\angle QRS+\angle SRY={180}^{\circ }$

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

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