The measure of arc xyz is 296 degrees. what is the measure of angle xzw, the tangent-chord angle?

a: 296
b: 148
c: 116
d: 206

Let O be the center of the circle.

Reflex angle XOZ = 296°
Obtuse angle XOZ = 360° - 296° = 64°
Triangle XOZ is an isosceles triangle.

∴ Angle OZX = (180° - 64°) / 2 = 58°
(Base angle of an isosceles triangle)

Angle OZW = 90°
(Tangent to circumference of circle)

Angle XZW = 90° + 58° = 148°

Answer is B.