In the given figure, straight lines AB and CD intersect at O.
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 $]$

$\Rightarrow 3 \phi+\phi=180^{\circ} \quad[\because \theta=3 \phi]$

$\Rightarrow 4 \phi=180^{\circ}$

$\Rightarrow \phi=45^{\circ}$