Question

What is the measure of ABC?

Answer 1

the answer is A but i'm depending on my self

Answer 2

D. 37°

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 =
`((1)/(2))` 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 =
`((1)/(2))` ∠AOC

if you replace the value, you get:

m∠ABC =
`((1)/(2))`(74°)

m∠ABC = 37°

so answer is D. 37°