Question:
In the below fig, lines PQ and RS intersect each other at point O. If ∠POR: ∠ROQ = 5: 7. Find all the angles.
Solution:
Given
∠POR and ∠ROP is linear pair
∠POR + ∠ROP = 180°
Given that
∠POR: ∠ROQ = 5:7
Hence, POR = (5/12) × 180 = 75
Similarly ROQ = (7/7 + 5) × 180 = 105
Now POS = ROQ = 105° [Vertically opposite angles]
Also, SOQ = POR = 75° [Vertically opposite angles]