Answer:
The measure of angle ABC is 34°.
Step-by-step explanation:
From the given figure it is clear that the measure of arc AC(minor) is 146 °.
Minor arc + Major arc = 360°
[tex]146+x=360[/tex]
[tex]x=360-146=214[/tex]
The measure of arc AC(major) is 214 °.
According to the properties of intercepted arc outside the circle, angle ABC is
[tex]\angle ABC=\frac{\text{Major arc AC}-\text{Minor arc AC}}{2}[/tex]
[tex]\angle ABC=\frac{214-146}{2}[/tex]
[tex]\angle ABC=\frac{68}{2}[/tex]
[tex]\angle ABC=34[/tex]
Therefore the measure of angle ABC is 34°.
