Question

In the given parallelogram $YOUR,\angle RUO={120}^o$ and $OY$ is extended to point S such that $\angle SRY={50}^o$. Find $\angle YSR$.

• A. ${90}^o$
• B. ${70}^o$
• C. ${80}^o$
• D. ${60}^o$

Answer 1

The correct option is B ${70}^o$

$YOUR$ is a parallelogram.

Using the property "Opposite angles of a parallelogram are equal."

We have $\angle RUO=\angle RYO={120}^{\circ }$

$\angle SYO={180}^{\circ }$ which is a straight line.

$\angle SYO=\angle SYR+\angle RYO$

$\Rightarrow {180}^{\circ }=\angle SYR+{120}^{\circ }$

$\Rightarrow \angle SYR={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

From $△SYR,\angle RSY+\angle RYS+\angle YRS={180}^{\circ }$

$\Rightarrow \angle RSY+{60}^{\circ }+{50}^{\circ }={180}^{\circ }$

$\Rightarrow \angle RSY={180}^{\circ }-{110}^{\circ }={70}^{\circ }$