- A65°
- B40°
- C85°
- D75°
Step-by-Step Solution
By the alternate-segment theorem, the angle in the alternate segment equals the tangent–chord angle, so angle ACB = 65°. In triangle ABC, angle BAC = 180° − 65° − 40° = 75°.
Answer: D) 75°
A line PAQ is tangent to a circle at the point A, and AB is a chord of that circle. The angle between the tangent ray AQ and the chord AB is 65°. C is a point of the circle lying in the alternate segment, that is, on the opposite side of chord AB from the ray AQ. If angle ABC = 40°, what is the measure of angle BAC?
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