Question

what is the measure of (overarc{ac})?

Explanation:

Step1: Identify the type of angle

The angle at \( B \) is an inscribed angle? Wait, no, \( B \) seems to be on the circle? Wait, no, looking at the diagram, \( BA \) is a diameter? Wait, no, the key here: the measure of an inscribed angle is half the measure of its intercepted arc. Wait, no, actually, if \( \angle ABC = 44^\circ \), and we need to find the measure of arc \( AC \). Wait, no, maybe \( BA \) is a diameter? Wait, no, let's think again. Wait, the angle at \( B \) is an inscribed angle, and the arc \( AC \) is intercepted by angle \( ABC \). Wait, no, the formula for an inscribed angle: the measure of an inscribed angle is half the measure of its intercepted arc. Wait, no, if the angle is at the circumference, then the arc it intercepts is twice the angle. Wait, no, let's correct: the measure of an inscribed angle (angle with vertex on the circle) is half the measure of its intercepted arc. So if \( \angle ABC = 44^\circ \), then the arc \( AC \) would be \( 2 \times 44^\circ = 88^\circ \)? Wait, no, wait, maybe I got it reversed. Wait, no, let's check: the inscribed angle theorem states that an angle \( \theta \) subtended by an arc at the circumference is half the central angle subtended by the same arc. Wait, but in the diagram, is \( B \) on the circle? Yes, \( B \) is on the circle, so \( \angle ABC \) is an inscribed angle, and it intercepts arc \( AC \). Therefore, the measure of arc \( AC \) is twice the measure of \( \angle ABC \). So \( \text{Arc } AC = 2 \times 44^\circ = 88^\circ \).

Step2: Calculate the arc measure

Using the inscribed angle theorem: \( \text{Measure of arc } AC = 2 \times \text{Measure of } \angle ABC \)
Given \( \angle ABC = 44^\circ \), so \( \text{Arc } AC = 2 \times 44^\circ = 88^\circ \)

Answer:

\( 88^\circ \) (corresponding to the first option)