If angle ABC measures 124 degrees What is the measure of arc AC'?

If you are considering a circle, where the central angle is 124o of 360, then, we have the diameter, 2r, multiplied by pi, and then a twist, multiplied by the ratio of the angle (ABC in this case) and 360 (the total measure of the circle). Therefore, we have:

2pi(r) * (124/360) = 2pi(r)*(31/90) = 31/45 pi * r.

However, with the information you provided, we are unable to deduce a complete numerical answer for arc AC.

However, considering you meant that the point B is located on the circumference of the circle, then that is a different matter.

We now have a circle, with the diameter shown, and chord BC is given, we can draw a line from the center of the circle where the diameter is, and connects with point C. Thus, we have another radius section (DC, given D is the center). Then, we have the radius stretching from point D to B. Thus, we have an isosceles triangle. This means that angle C = angle B. Now, because there is 180 degrees in a triangle, and angle C = angle B, we have:

180 - 2a = a2

Now, a line is also 180 degrees so subtracting 180 degrees, we have:

180 - (180 - 2a) = Angle D

180 - 180 + 2a = Angle D

2a = Angle D

Now, we know that a is the angle, thus, subsituting in the equation, we have 2(124) = 248o.

Using the above information, we could multiply by 2 (248 is twice of 124), thus giving 62/45 * pi* r. (2pi*r * 248/360 = 2pi * r * 31/45 = pi * r * 62/45)