Question

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

• A. $\angle QRS={750}^o$
• B. $\angle QRS={60}^o$
• C. $\angle QRS={45}^o$
• D. $\angle QRS={30}^o$

Answer 1

The correct option is B $\angle QRS={60}^o$

Through R, we draw XRYPQ.
XRYST(PRST)
QRX+${110}^o$ =${180}^o$
and YRS+${130}^o$=${180}^o$
QRX=${70}^o$
and YRS=${50}^o$
Now, QRX+QRS+YRS=${180}^o$
${70}^o$ +QRS+ ${50}^o$=${180}^o$
QRS=${60}^o$