Answer:
x = 11
Explanation:
The measure of an arc of a circle is twice the measure of the inscribed angle that intercepts the arc.
m(arc)YZ = 2 × 59°
m(arc)YZ = 118°
A full circle has arc measure 360°.
m(arc)ZX + m(arc)XY + m(arc)YZ = 360°
75° + (17x - 20)° + 118° = 360°
75 + 17x - 20 + 118 = 360
17x + 173 = 360
17x = 187
x = 11