Question

lines PQ and RS intersect each other at point O. If <POR : <ROQ = 5 : 7, FIND ALL THE ANGLES..​

Answer 1

SOLUTION :

Ratio of $\angle$ POR and $\angle$ ROQ is 5:7

Let common factor be x.

Now,

As we can see,

$\angle$ POR and $\angle$ POR = 180°    ( linear pair)

⇒ 5x + 7x = 180°

⇒ 12x = 180°

⇒ x = $\dfrac{180°}{12}$

 $\bf\huge\boxed{x\:=\:15°}$

So,   $\angle$ POR = 5 × 15 = 75°

      $\angle$ ROQ = 7 × 15 = 105°

Therefore,

$\angle$ SOQ = 75° ( Vertically opposite angle )

$\angle$ POS = 105° ( vertically opposite angle )

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$\huge{\mathfrak{\red{BE\:BRAINLY:)}}}$