# In the given figure, AOB is a straight line.

Question:

In the given figure, AOB is a straight line. If ∠AOC = 4x° and ∠BOC = 5x°, then ∠AOC = ?
(a) 40°
(b) 60°
(c) 80°
(d) 100°

Solution:

(c) 80°

We have

$\angle A O C+\angle B O C=180^{\circ} \quad$ [Since $A O B$ is a straight line]

$\Rightarrow 4 x+5 x=180^{\circ}$

$\Rightarrow 9 x=180^{\circ}$

$\Rightarrow x=20^{\circ}$

$\therefore \angle A O C=4 \times 20^{\circ}=80^{\circ}$