Question

In the given figure, straight lines AB and CD intrsect at O. If $\angle AOC=\varphi ,\angle BOC=\theta$ and $\theta =3\varphi$, then $\varphi =?$

$\left(a\right){30}^{\circ }$

$\left(b\right){40}^{\circ }$

$\left(c\right){45}^{\circ }$

$\left(d\right){60}^{\circ }$

Answer 1

ANSWER:
$\left(c\right){45}^{\circ }$
We have :
$\theta +\varphi ={180}^{\circ }\because AODisastraightline\Rightarrow 3\varphi +\varphi ={180}^{\circ }\because \theta =3\varphi \Rightarrow 4\varphi ={180}^{\circ }\Rightarrow \varphi ={45}^{\circ }$