Question

In the figure, it is given that $\angle POQ={70}^0$ and the ray OB bisects $\angle AOQ$. Find $\angle BOP$ and reflex $\angle AOB$.

• A. ${125}^{\circ }and{305}^{\circ }$
• B. ${105}^{\circ }and{325}^{\circ }$
• C. ${100}^{\circ }and{320}^{\circ }$
• D. None of these

Answer 1

The correct option is A ${125}^{\circ }and{305}^{\circ }$

Since AOP is a line,
$\therefore \angle AOQ+\angle POQ={180}^0$
$\Rightarrow \angle AOQ+{70}^0={180}^0$
$\Rightarrow \angle AOQ={110}^0$

Since ray OB bisects $\angle AOQ$
$\therefore \angle AOB=\angle BOQ=\frac{1}{2}\angle AOQ$
$\Rightarrow \angle AOB=\angle BOQ=\frac{1}{2}\times {110}^0$
$\Rightarrow \angle AOB=\angle BOQ={55}^0$
$\angle BOP=\angle BOQ+\angle QOP$
$={55}^0+{70}^0$
$\Rightarrow \angle BOP={125}^0$
Now,$\left(\text{Reflex}\angle AOB\right)+\angle AOB={360}^0$
$\Rightarrow \text{Reflex}\angle AOB+{55}^0={360}^0$
$\Rightarrow \text{Reflex}\angle AOB={305}^0$

So, option a is correct.