Question

Find the value of Y [Inscribed Angle]

Answer 1

Check the picture below.

Answer 2

x = 60°

Explanation:

From ΔOPQ,

∠OPQ = 120° [ angle at the center inscribed by arc PQ ]

PQ ≅ OQ

so opposite angles to PQ and OQ will be equal

∠OPQ ≅ ∠OQP

∠OPQ + ∠OQP + ∠POQ = 180°

∠OPQ + ∠OPQ + 120 = 180°

2∠OPQ = 180 - 120 = 60°

∠OPQ = 30°

Since radius OP is perpendicular to tangent.

so ∠OPQ + Y = 90°

y + 30° = 90°

y = 90 - 30 = 60°

Answer x = 60°