Question

In the given figure, CD and AE are straight lines.

Find the value of ∠AOB.

• A. 85°
• B. 90°
• C. 95°
• D. 105°

Answer 1

The correct option is D 105°

From the figure:


∠ AOD and ∠COE are vertical angles.

We know, vertical angles are congruent.

$\therefore \angle AOD=\angle COE={140}^{\circ }$

Again,
$\angle AOD=\angle AOB+\angle BOD$

So,
${140}^{\circ }=\angle AOB+{35}^{\circ }$

$\Rightarrow \angle AOB={140}^{\circ }-{35}^{\circ }$

$\Rightarrow \angle AOB={105}^{\circ }$

So, the value of ∠AOB is 105°.