Mathematics

# In Fig., PQ and RS intersect each other at point O. If $\angle POR : \angle ROQ = 5:7,$ find all the angles.

##### SOLUTION
We have. $\angle POR : \angle ROQ = 5 : 7$

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

Since $\angle POR$ and $\angle ROQ$ form a linear pair.

$\therefore \angle POR + \angle ROQ = 180^{\circ}\Rightarrow 5x+7x = 180^{\circ} \Rightarrow x = 15^{\circ}$

$\therefore \angle POR = \left ( 5 \times 15 \right )^{\circ} = 75^{\circ}$ and

$\angle ROQ = \left ( 7 \times 15 \right )^{\circ} = 105^{\circ}$

But, $\angle QOS = \angle POR$ and $\angle POS = \angle ROQ$ [vertically opposite angles]

$\therefore \angle QOS = 75^{\circ}$ and $\angle POS = 105^{\circ}$

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87

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