Question

In figure, lines PQ and RS intersect each of
point O. If POR: POS = 5:7 find all angles​

Answer 1

Step-by-step explanation:

por+pos = 180°

5x+4x. = 180°

12x=180°

x=180/12

x = 15

POR = 5X = 5*15 = 75

POS = 7X = 7*15 = 105

Answer 2

Solution:

∠POR + ∠ROQ = 180° (linear pair of angles)

But,

∠POR : ∠ROQ = 5:7 (Given)

Therefore,

∠POR = 5/12 ×180° = 75°

Similarly,

∠ROQ = 7/12 × 180° = 105°

Now,

∠POS = ∠ROQ = 105° (Vertically opp. angles)

and,

∠SOQ = ∠POR = 75° (Vertically opp. angles)