In the figure below, lines RS and PQ intersect each other at point O. If ∠POR: ∠ROQ = 11:13, find ∠SOQ.
∠POR + ∠ROQ = 180∘ (linear pair of angles)
but, ∠POR : ∠ROQ = 11:13 (given)
∠POR = 1124 × 180∘ = (1652)∘
Similarly, ∠ROQ = 1324 × 180∘ = (1952)∘
Now, ∠POS = ∠ROQ = (1952)∘ (vertically opposite angle)
And, ∠SOQ = ∠POR= (1652)∘ (vertically opposite angle)