Answer:
C. [tex]56^{\circ}[/tex]
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the measure of arc AC.
We will use tangent-secant theorem, which states that the angle formed by a tangent to a circle and a chord is equal to half the angle measure of the intercepted arc.
Using above theorem we can set an equation to find measure of arc AC as:
[tex]m\angle BAC=\frac{1}{2}\times \text{ Measure of arc AC}[/tex]
[tex]28^{\circ}=\frac{1}{2}\times \text{ Measure of arc AC}[/tex]
Multiplying both sides of our equation by 2, we will get,
[tex]2*28^{\circ}=\frac{1}{2}*2\times \text{ Measure of arc AC}[/tex]
[tex]56^{\circ}=\text{ Measure of arc AC}[/tex]
Therefore, the measure of arc AC is 56 degrees and option C is the correct choice.
