Question 38
Circle TheoremsIn the figure above, XR and YQ are tangents to the circle YZXP. If ZX̂R = 45° and YẐX = 55°, find ZŶQ
- A.135°
- B.125°
- C.100°
- D.90°
Show the answer and explanation
Answer: C (100°)
Explanation
The angle between a tangent and a chord equals the angle in the alternate segment. So angle ZYX = angle ZXR = 45°, and in triangle XYZ angle YXZ = 180° − 45° − 55° = 80°. The angle between YZ and the tangent on the other side of Y is 80°, so angle ZYQ = 180° − 80° = 100°.