Question

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

• A. $126°$
• B. $144°$
• C. $136°$
• D. $154°$

Answer 1

The correct option is B

$144°$

Explanation for the correct option:

Step 1: Compute the value of $x$ and $y$.

The Sum of all angles about a straight line given in the figure is equal to $180°.$

$PQ$ is a straight line.

Then, $\angle POR+\angle ROT+\angle TOQ=180°$

Given, $x:y=3:2$

Assume that $x=3a,y=2a$.

That is

$90°+3a+2a=180°$

$90°+5a=180°$

$5a=180°–90°$

$5a=90°$

$a=\frac{90}{5}$

$a=18°$

So, $x=3a=3\times 18=54°$

and $y=2a=2\times 18=36°$

Step 2: Compute the required value.

Then,$z+y=180°$

$z+36°=180°$

$z=180°–36°$

$z=144°$

Hence, option $B$ is the correct answer.