In circle q shown below, the marc ur is 199° and the marc rs is 84°. circle with center q with a tangent line touching at point u and extending to point t. a secant line through rs and extending to point t. what is the measure of ∠stu? a. 57.5° b. 61° c. 138° d. 141.5°

Please see the attached figure.
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As shown:
TU is a tangent line to the circle touching at point U
∴ ∠ QUT =90°   (1)

the mArc UR is 199° ⇒⇒⇒ ∠RQU = 199° (largest arc)
and the mArc RS is 84°⇒⇒⇒ ∠RQS = 84°

∴∠ SQU = 360° - (199°+84°) = 360° - 283° = 77°

 Δ RSQ is isosceles triangle because QR = QS = radius of the circle Q
∴∠QRS = 0.5 (180° - 84° ) = 48° (2)

∵ The sum of angels of the shape RQUT = 360°
∠R = 48°    (from 2)
∠Q = 360° - 199° = 161°
∠U = 90°    (from 1)
∴∠T = 360° - (∠R+∠Q+∠U)
        = 360° - (48°+161°+90°) = 61°

The correct answer is option (B)
B. 61°