To find the measure of arc $AC$ in the circle, let's analyze the given information:

1. The circle has points $A$, $B$, and $C$ lying on its circumference.
2. $\angle BAC = 44^\circ$, as indicated.

Step-by-Step Solution:

In a circle, an inscribed angle (like $\angle BAC$) is equal to half the measure of the arc it intercepts. Here, $\angle BAC$ intercepts arc $AC$.

Using the inscribed angle theorem: $\text{Measure of arc } AC = 2 \times \text{measure of } \angle BAC$

Substituting the given angle measure: $\text{Measure of arc } AC = 2 \times 44^\circ = 88^\circ$

Answer:

The measure of $\overarc{AC}$ is 88°.

So, the correct answer is:

• D. 88°

Would you like a further breakdown of the inscribed angle theorem or have any other questions?

Related Questions:

1. How does the inscribed angle theorem apply to other types of arcs?
2. What would the measure of arc $BC$ be if $\angle ABC$ is known?
3. How would the solution change if $\angle BAC$ was given as 22°?
4. Can an inscribed angle be equal to its intercepted arc?
5. How would this problem change if the arc was a major arc instead?

Tip:

Remember, for any inscribed angle, the intercepted arc is always twice the angle. This rule is very useful in solving problems involving circles.