Question

Question 150
In the given parallelogram YOUR, $\angle RUO={120}^{\circ }$ and OY is extended to point S, such that $\angle SRY={50}^{\circ }$. Find $\angle YSR$.

Answer 1

Given, $\angle RUO={120}^{\circ }$ and $\angle SRY={50}^{\circ }$
$\angle RYO=\angle RUO={120}^{\circ }$ [$\because$ opposite angles of a parallelogram]
Now, $\angle SYR={180}^{\circ }-\angle RYO$ [linear pair]
$={180}^{\circ }-{120}^{\circ }={60}^{\circ }$
In $\Delta SRY$,
By the angle sum property of a triangle, $\angle SRY+\angle RYS+\angle YSR={180}^{\circ }$
$\Rightarrow {50}^{\circ }+{60}^{\circ }+\angle YSR={180}^{\circ }\Rightarrow \angle YSR={180}^{\circ }-({50}^{\circ }+{60}^{\circ })={70}^{\circ }$.