Lines RS and PQ intersect each other at point O. If ∠POR:∠ROQ = 11:13, ∠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)∘=82.5∘ (vertically opposite angle)