Answer:
m∠ABC = 120°
Explanation:
Consider the case where point C is on the circle and long arc AC has measure 240°. Then ∠ABC is an inscribed angle, and its measure is half the measure of the intercepted arc, so is 120°.
This is still true even when point B and point C are on top of each other and BC is a tangent to the circle. That is the case shown here, so m∠ABC = 120°.