Question

Find the measure of the angle ∠AOB in the given figure.

Are the angles ∠AOB and ∠BOC in the given figure complementary angles?

• A. 45° , Yes
• B. 55° , No
• C. 45° , No
• D. 55° , Yes

Answer 1

The correct option is A 45° , Yes


In the given figure,
∠DOC = 180° (straight angle)

So, we can write:
$\angle AOD+\angle AOC={180}^{\circ }$
$\Rightarrow \angle AOC={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

Now we observe,
$\angle AOC=\angle AOB+\angle BOC\Rightarrow {90}^{\circ }$

Hence, angles ∠AOB and ∠BOC are complementary angles.

∠BOC is given as 45°

Also,
Sum of complementary angles = 90°

So,
$\angle AOB+\angle BOC={90}^{\circ }$
$\Rightarrow \angle AOB+{45}^{\circ }={90}^{\circ }$
$\Rightarrow \angle AOB={90}^{\circ }-{45}^{\circ }={45}^{\circ }$ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->