Question

$AOB$ is a straight line. If $\angle POB$ is half of $\angle AOP$, what is the measure of $\angle POB$?

• A. 60°
• B. 30°
• C. 45°
• D. 55°

Answer 1

The correct option is A 60°

Given AOB is a straight line.
Hence,
$\angle AOB+\angle POB=180°\left(Linearpair\right)...\left(i\right)$

$\angle POB=\frac{1}{2}\angle AOB\left(Given\right)...\left(ii\right)$

Substituting (ii) in (i),
$\angle AOB+\frac{1}{2}\angle AOB=180°$
$\Rightarrow \frac{3}{2}\angle AOB=180°$
$\Rightarrow 3\times \angle AOB=180°\times 2=360°$
$\Rightarrow \angle AOB=\frac{360°}{3}=120°$

Then from (ii),
$\angle POB=\frac{1}{2}\times 120°=60°$