"
">

In the figure, lines $PQ$ and $RS$ intersect each other at point $O$. If $\angle POR : \angle ROQ = 5 : 7$. Find all the angles."

Academic Mathematics NCERT Class 9

Given:

Lines $PQ$ and $RS$ intersect each other at point $O$.

$\angle POR : \angle ROQ = 5 : 7$

To do:

We have to find all the angles.

Solution:

We know that,

Vertically opposite angles are equal.

Therefore,

$\angle POR = \angle QOS$ and $\angle ROQ = \angle POS$

$\angle POR : \angle ROQ = 5:7$

Let $\angle POR = 5x$ and $\angle ROQ = 7x$

$\angle POR + \angle ROQ = 180^o$ (Linear pair)

$5x + 7x = 180^o$

$12x = 180^o$

$x = \frac{180^o}{12}$

$x= 15^o$

Therefore,

$\angle POR = 5x = 5(15^o) = 75^o$

$\angle ROQ = 7x = 7(15^o) = 105^o$

$\angle QOS = POR = 75^o$

$\angle POS = \angle ROQ = 105^o$.

Updated on: 10-Oct-2022

55 Views

Kickstart Your Career

Get certified by completing the course

Advertisements