Answer:
x = 38
Explanation:
The external angle of a circle = ½ of the difference of the measures of the intercepted arcs. Thus:
m<S = ½(arc UV - arc TW)
34 = ½[(3x - 2) - (x + 6)]
34 = ½[3x - 2 - x - 6] (distributive property)
Add like terms
34 = ½[2x - 8]
Multiply both sides by 2
2*34 = 2x - 8
68 = 2x - 8
68 + 8 = 2x - 8 + 8
76 = 2x
Divide both sides by 2
76/2 = 2x/2
38 = x
x = 38