Question

In figure, lines $PQ$ and $ST$ intersect at $O$. If $\angle POR={90}^o$ and $x:y=3:2$, then $z$ is equal to

• A. ${126}^o$
• B. ${144}^o$
• C. ${136}^o$
• D. ${154}^o$

Answer 1

The correct option is B ${144}^o$

We can see in the given figure, $PQ$ is a straight line

$\therefore \angle POR+ROT+\angle TOQ={180}^o$

$\Rightarrow {90}^o+x+y={180}^o$

$\Rightarrow x+y={90}^o$

$\Rightarrow x+y={90}^o$ ...(1)

Given that, $\frac{x}{y}=\frac{3}{2}$

Let $x=3K$ and $y=2K$

From equation (1)

$\Rightarrow 3K+2K={90}^o$

$\Rightarrow K=\frac{{90}^o}{5}$

$\Rightarrow K={18}^o$

$\therefore y=2\times {18}^o={36}^o$

Now, $SOT$ is a straight line

$\Rightarrow z+y={180}^o$

$\Rightarrow z+{36}^o={180}^o$

$\Rightarrow z={180}^o-{36}^o$

$\Rightarrow z={144}^o$

Hence, Option $\left(B\right)$ is correct.