Answer:
x = 12°
Welcome to concept of Inscribed Angle theorem
In the diagram shown above, the inscribed angle m∠SUT intercepts the diameter ST.
Then,
m∠SUT = 90°
In Δ SUT,
m∠S + m∠U + m∠T = 180°
Substitute.
m∠S + 90° + 43° = 180°
m∠S + 133° = 180°
Subtract 133° from each side.
m∠S = 47°
m∠UST = 47°
By Inscribed Angle Theorem,
m∠arc UT = 2 ⋅ m∠UST
Substitute.
(9x - 14)° = 2 ⋅ 47°
(9x - 14)° = 94°
9x - 14 = 94
Add 14 to each side.
9x = 108
Divide each side by 9
x = 12
Hence, we get as x = 12°