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]
$\Rightarrow 4 x+5 x=180^{\circ}$
$\Rightarrow 9 x=180^{\circ}$
$\Rightarrow x=20^{\circ}$
$\therefore \angle A O C=4 \times 20^{\circ}=80^{\circ}$
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