Question:
In the given figure, straight lines $A B$ and $C D$ intersect at $O$. If $\angle A O C=\Phi, \angle B O C=\theta$ and $\theta=3 \phi$, then $\phi=$ ?
(a) 30°
(b) 40°
(c) 45°
(d) 60°
Solution:
(c) 45°
We have:
$\theta+\phi=180^{\circ} \quad[\because A O D$ is a straight line $]$
$\Rightarrow 3 \phi+\phi=180^{\circ} \quad[\because \theta=3 \phi]$
$\Rightarrow 4 \phi=180^{\circ}$
$\Rightarrow \phi=45^{\circ}$
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