Question

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

Answer 1

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.