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Question
In the figure given below, O is the center of the circle and SP is a tangent. If ∠SRT = 65°, find the value of x, y and Z.
Solution
TS ⊥ SP,
`=>` ∠TSR = 90°
In ΔTSR,
∠TSR + ∠TRS + ∠RTS = 180°
`=>` 90° + 65° + x = 180°
`=>` x = 180° – 90° – 65°
`=>` x = 25°
Now, y = 2x ...(Angle subtended at the center is double that of the angle subtended by the arc at the same centre)
`=>` y = 2 × 25°
`=>` y = 50°
In ΔOSP,
∠OSP + ∠SPO + ∠POS = 180°
`=>` 90° + z + 50° = 180°
`=>` z = 180° – 140°
`=>` z = 40°
Hence, x = 25°, y = 50° and z = 40°
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