PS and PT are two tangents from a point P outside the circle with center O. If S and T are points on the circle such that ∠SPT = 130°, then the degree measure of ∠OST is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 65°.
∠SPT = 130°
⇒ ∠TOS = 180° - ∠SPT = 180° - 130° = 50°
Triangle SOT is an isosceles triagnle
∠OST = ∠STO
∠TOS + ∠OST + ∠STO = 180°
⇒ 50° + ∠OST + ∠OST = 180°
⇒ 2∠OST = 180° - 50°
∠OST = 130°/2 = 65°