The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X: The figure shows a circle with points A and B on it and point C outside it. Side BC of triangle ABC intersects the circle at po

What is the measure of angle ACB? (6 points)

23°

32°

46°

16°

The correct option is C. 46°

Step-by-step explanation:

First find the measure of the arc AX
Now, Arc measure is twice the angle formed in the segment by the same arc
⇒ Measure AX = 2 × ∠ABX
⇒ Measure AX = 2 × 32°
⇒ Measure AX = 64°
Now we will use tangent-secant angle formula to find the measure of ∠ACB as ∠ACB is formed by tangent AC and secant BC outside our given circle.
⇒ ∠ACB = 0.5 × (Measure of major arc - Measure of minor arc)
⇒ ∠ACB = 0.5 × (156° - 64°)
⇒ ∠ACB = 0.5 × 92°
⇒ ACB = 46°
Therefore, The correct option is C. 46°