Question

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

Answer 1

Draw a line through R parallel to PQ.

$\angle QRX={180}^o-{110}^o={70}^o$

$\angle SRY={180}^o-{130}^o={50}^o$

$\angle QRS={180}^o-(\angle QRX+\angle SRY)$

$={180}^o-({70}^o+{50}^o)$

$={110}^o-{50}^o$

$={60}^o$

$\therefore \angle QRS={60}^o$.