Question

In figure, $ \angle ROS$ is a right angle and $ \angle POR$ and $ \angle QOS$ are in the ratio $ 1:5$. Then, $ \angle QOS$ measures:

• A. $150°$
• B. $75°$
• C. $45°$
• D. $60°$

Answer 1

The correct option is B

$75°$

Step 1: State the given data and suppose variable

It is given that $\angle ROS=90°$

And, $\angle POR:\angle QOS=1:5$

Let, $\angle POR=x$

Then, $\angle QOS=5x$ $...\left(\mathrm{i}\right)$

Step 2: Calculate the value of $x$

As we know, the angles lying on the same side of a straight line are supplementary.

i.e., the sum of the angles lying on the same side of a straight line is $180°$.

So, $\angle POR+\angle ROS+\angle QOS=180°$

$\Rightarrow$ $x+90°+5x=180°$

$\Rightarrow$ $6x+90°=180°$

$\Rightarrow$ $6x=180°-90°$

$\Rightarrow$ $6x=90°$

$\Rightarrow$ $x=\frac{90°}{6}$

$\Rightarrow$ $x=15°$

Step 3: Calculate the value of $\angle QOS$

On substituting this value of $x$ in the equation $\left(\mathrm{i}\right)$, we get,

$\Rightarrow$ $\angle QOS=5x$

$\Rightarrow \angle QOS=5\times 15°$

$\Rightarrow \angle QOS=75°$

Hence, $\angle QOS=75°$, so, option (B) is the correct option.