Question

In the given figure, $PQ$ and $RS$ are two lines intersecting each other at point ${}^{\prime }{O}^{\prime }$. If $\angle POS={90}^{\circ }$. Find the value of $x,y$ and $z$.

Answer 1

As shown in fig two lines $PQ$ and $RS$ are intersect to each other at point $O$

Given that angle $POS={90}^0$

Now , $\angle ROQ=\angle POS={90}^0=x$ vertically opposite angle

$y=\angle SOQ={180}^0-\angle PO$

$={180}^0-{90}^0$

$={90}^0$

$z=\angle POR=\angle SOQ={90}^0$ vertically opposite angle