Question

Observe the following figure and find the measure of angle ∠AOD.

• A. 100°
• B. 120°
• C. 140°
• D. 150°

Answer 1

The correct option is C 140°



We know,

$\angle CO{C}^{\prime }={180}^{\circ }\text{[straight angle]}$

So,
$\angle AO{C}^{\prime }+\angle AOB+\angle BOC={180}^{\circ }$

Substituting the given values, we get:

$\angle AO{C}^{\prime }+{50}^{\circ }+{40}^{\circ }={180}^{\circ }$

$\Rightarrow \angle AO{C}^{\prime }={180}^{\circ }-({50}^{\circ }+{40}^{\circ })$

$\Rightarrow \angle AO{C}^{\prime }={180}^{\circ }-{90}^{\circ }$

$\Rightarrow \angle AO{C}^{\prime }={90}^{\circ }$

Similarly,

$\angle C^{\prime }OD+\angle DOC={180}^{\circ }\text{[straight angle]}$

$\Rightarrow \angle C^{\prime }OD+{130}^{\circ }={180}^{\circ }$

$\Rightarrow \angle C^{\prime }OD={180}^{\circ }-{130}^{\circ }$

$\Rightarrow \angle C^{\prime }OD={50}^{\circ }$

We know,
$\angle AOD=\angle AO{C}^{\prime }+\angle C^{\prime }OD$

$\angle AOD={90}^{\circ }+{50}^{\circ }$

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