Answer:
x = 38
Step-by-step explanation:
The measure of a vertex angle outside a circle = ½(difference of intercepted arcs)
Thus:
m<S = ½(UV - TW)
m<S = 34°
UV = (3x - 2)°
TW = (x + 6)°
Plug in the values into the equation
34 = ½((3x - 2) - (x + 6))
34 = ½(3x - 2 - x - 6)
34 = ½(2x - 8)
Multiply both sides by 2
34*2 = 2x - 8
68 = 2x - 8
68 + 8 = 2x (addition property of equality)
76 = 2x
76/2 = x (division property of equality)
38 = x
x = 38
