Question
AC is tangent to circle O at point A, and mAB = 59. What is m/ACB?
C
A
B
(not drawn to scale)
A 121
B 21
C 31
D 29
C
A
B
(not drawn to scale)
A 121
B 21
C 31
D 29
Answers
GPT 3.5
C 31
Since AC is tangent to the circle at point A, tangent lines are perpendicular to the radius at the point of tangency. Therefore, triangle ABC is a right triangle with right angle at C. The sum of the angles in a triangle is 180 degrees, so m∠B = 90 degrees and m∠A = 180 - 90 - 59 = 31 degrees. Therefore, m∠ACB = 31 degrees.
Since AC is tangent to the circle at point A, tangent lines are perpendicular to the radius at the point of tangency. Therefore, triangle ABC is a right triangle with right angle at C. The sum of the angles in a triangle is 180 degrees, so m∠B = 90 degrees and m∠A = 180 - 90 - 59 = 31 degrees. Therefore, m∠ACB = 31 degrees.