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.

Answer 1

$YOUR$ is a parallelogram.

$\angle RUO={120}^o$

$\Rightarrow$ $RUO=\angle RYO$ [ Opposite angles in parallelogram are equal ]

$\therefore$ $\angle RYO={120}^o$

$\Rightarrow$ $\angle RYS+\angle RYO={180}^o$ [ Linear pair ]

$\Rightarrow$ ${120}^o+\angle RYO={180}^o$

$\therefore$ $\angle RYO={60}^o$

In $△RSY,$

$\Rightarrow$ $\angle SRY+\angle RYS+\angle YSR={180}^o$ [ Sum of angles in triangle is ${180}^o$ ]

$\Rightarrow$ ${50}^o+{60}^o+\angle YSR={180}^o$

$\Rightarrow$ ${110}^o+\angle YSR={180}^o$

$\therefore$ $\angle YSR={70}^o$.