Question

RS and RT are tangents to the circle center o. Angle SRT=40 degrees. What is the size of angle SUT

Answer 1

Answer: is c (70 degrees) I hope it helps anyone.

Step-by-step explanation:

RS is a tangent ⇒ ∠OSR = 90°

RT is a tangent ⇒ ∠OTR = 90°

OSRT is a quadrilateral, so has an angle sum of 360°

⇒ ∠OSR + ∠SRT + ∠OTR + ∠SOT = 360°

⇒ 90° + 40° + 90° + ∠SOT = 360°

⇒ 220° + ∠SOT = 360°

⇒ ∠SOT = 140°

Now use the Angle at the Center Theorem

∠SUT = ½ × ∠SOT = ½ × 140° = 70°