Answer:
D. 37°
Step-by-step explanation:
The angle ∠ABC is an inscribed angle because is formed by two chords that have a common end point (chord AB, chord CB), where point B is the vertex.
So, the inscribed angle theorem says that the measure of an inscribed angle is half the measure of the intercepted arc.
Thus:
measure ∠ABC = [tex](\frac{1}{2})[/tex] measure∠AOC
where ∠AOC is the central angle, that is, the angle with the vertex at the center of the circle.
The graph shows that the measure of angle ∠AOC is equal to 74°, therefore:
m∠ABC = [tex](\frac{1}{2})[/tex] ∠AOC
if you replace the value, you get:
m∠ABC = [tex](\frac{1}{2})[/tex](74°)
m∠ABC = 37°
so answer is D. 37°
