Given,
∠POR and ∠ROP is linear pair
∠POR + ∠ROP = 180°
Given that,
∠POR = ∠ROQ = 5: 7
Therefore,
∠POR = \(\frac{5}{12}\) × 180° = 75°
Similarly,
∠ROQ = 125°
Now,
∠POS = ∠ROQ = 125°(Vertically opposite angles)
Therefore,
∠SOQ = ∠POR = 75°(Vertically opposite angles)