Question

22.In the given figure, lines PQ and RS intersect each other at point O. If∠ POR : ∠ ROQ = 5 : 7, find ∠ POS.​

Answer 1

Answer:

105 is answer

please follow me .....

Answer 2

$\bf{\star\:\:{\red{\underline{\red{\underline{\blue{\huge{Given}}}}}}}}$

• Lines PQ and RS intersect each other at point O.
• $\sf{\angle POR : \angle ROQ = 5:7}$

$\bf{\star\:\:{\underline{\underline{\red{\huge{To\:Find}}}}}}$

$\sf{\angle POS}$

$\bf{\star\:\:{\purple{\underline{\purple{\underline{\green{\huge{Assumption}}}}}}}}$

Let the ratio constant be x

Therefore,

$\sf{\angle POR : \angle ROQ = 5x:7x}$

$\bf{\star\:\:{\underline{\underline{\pink{\huge{Solution}}}}}}$

In the figure,

$\sf{\angle POR + \angle ROQ = 180^\circ\:\:\:\:\:\:\:\:\:\:[Linear\:Pair]}$

= $\sf{5x + 7x = 180^\circ}$

= $\sf{12x = 180^\circ}$

= $\sf{x = \dfrac{180}{12}}$

= $\sf{x = 15}$

Now,

Calculating the measure of the angles POR and ROQ,

$\sf{\angle POR = 5x = 5\times 15 = 75^\circ}$

$\sf{\angle ROQ = 7x = 7\times 15 = 105^\circ}$

Now,

$\sf{\angle POS = \angle ROQ \:\:\:\:\:\:\:\:\:\:\:\: [Vertically\:Opposite\:Angles]}$

Therefore,

$\sf{\angle POS = 105^\circ}$

______________________________________

$\sf{\star}$ Note:-

When two lines intersect each other at a point,

• The vertically opposite angles are always equal. For example if we see the figure $\sf{\angle ROQ}$ is vertically opposite to $\sf{\angle POS}$ and $\sf{\angle POR}$ is vertically opposite to $\sf{\angle SOQ}$.
• The sum of all angles on a single straight line is always 180°.

______________________________________