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.

Answer 1

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°