The circle below has center t. suppose that m uv=138 degrees and that uw is tangent to the circle at u. find the following

answer:

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°

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step-by-step explanation: my bad its long @sf but i just wanna break it down like a blunt and pass it like a blunt im so dead lm@

10000

step-by-step explanation: divide by 2,