Question

In the given figure, straight lines $PQ$ and $RS$ intersect at $O$. If the magnitude of $\theta$ is 3 times that of $\varphi$, then $\angle \varphi$ is equal to:

• A. ${30}^o$
• B. ${40}^o$
• C. ${45}^o$
• D. ${60}^o$

Answer 1

Answer: (C)

${45}^o$

In the above figure straight lines $PQ$ and $RS$ intersect at $O$.

It is given that $\theta =3\varphi$ .....(1)

$\angle POR$ and $\angle QOR$ form linear pair of angles

Also $\angle POR=\varphi$ and $\angle QOR=\theta$

$\angle POR+\angle QOR=180$

$⟹\varphi +\theta =180$

$⟹\varphi +3\varphi =180$ .....(From 1)

$⟹4\varphi =180$

$⟹\varphi =\frac{180}{4}=45$

Hence, $\angle \varphi =45$