To find the measure of angle ABC, we can use the fact that the measure of an angle formed by two tangents drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.
In this case, the intercepted arc is arc AC, which measures 120°. The measure of the entire circle is 360°, so the measure of arc AOC (the arc opposite to AC) is:
- 360° – 120° = 240°
Now, we can apply the formula for the angle formed by the tangents:
- Angle ABC = ½ (measure of arc AOC – measure of arc AC)
- Angle ABC = ½ (240° – 120°)
- Angle ABC = ½ (120°)
- Angle ABC = 60°
Therefore, the measure of angle ABC is 60°.