Find the value of Y [Inscribed Angle]
2 answers:
Answer:
x = 60°
Step-by-step 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°
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