Question

In the below figure, lines PQ and RS intersect each other at point O. If
∠ POR: ∠ ROQ = 5: 7, find all the angles.

Answer 1

Step-by-step explanation:

∠POR : ∠ROQ = 5:7

Let ∠POR and ∠ROQ be 5x and 7x respectively

∠POR + ∠ROQ =180° (Linear pair)

5x+7x=180°

12x=180°

x=180/12

x=15

∠POR = 5x= 5×15 = 75°

∠ROQ = 7x =7×15=105°

∠QOS = ∠POR = 75° ( Vertically Opposite Angle)

∠POS = ∠ROQ = 105°( Vertically Opposite Angle)