In the diagram of circle O, what is the measure of abc? 34° 45° 68° 73°

Answer:A. [tex]m\angle ABC=34^{\circ}[/tex]Step-by-step explanation:We have been given a diagram. We are asked to find the measure of angle ABC.First of all, we will find measure of major arc AC by subtracting 146 from 360 degrees.[tex]\text{Measure of arc AC}=360^{\circ}-146^{\circ}[/tex][tex]\text{Measure of arc AC}=214^{\circ}[/tex]Now, we will use tangent-tangent angle theorem to solve for ABC.Tangent-Tangent angle theorem states that angle formed by two tangents outside a circle is half the difference of intercepted arcs.[tex]m\angle ABC=\frac{214^{\circ}-146^{\circ}}{2}[/tex][tex]m\angle ABC=\frac{68^{\circ}}{2}[/tex][tex]m\angle ABC=34^{\circ}[/tex]Therefore, the measure of angle ABC is 34 degrees and option A is the correct choice.