Answer:
D. 21
Step-by-step explanation:
Given:
m arc AC = 69
Segment AB is tangent to circle O at point A.
We need to find the ∠ ABC
Solution:
Now we can say that;
By inscribed angle theorem which states that;
"Central angle is equal to arc subtended by it."
m∠O = 69 (Central angle)
Also Given:
Segment AB is tangent to circle O at point A.
Now by radius tangent property which states that;
"Radius which touches to closet point on the tangent is always perpendicular."
so we can say that;
m∠OAB = 90
Now in Δ OAB.
m∠O = 69
m∠OAB = 90
Now we know that;
"Sum of all angles of triangle is 180."
m∠O + m∠OAB + m∠ABO = 180
Substituting the values we get;
Subtracting both side by 159 we get;
Now we can say that;
m∠ABO = m∠ ABC = 21 (same angles)
Hence m∠ ABC is 21.