In a adjoining figure there is a circle with center O. If Dc, diameter AB, and m∠AOC= 120 degree, then m∠ACD is?

To find the measure of angle ACD, we can use the properties of angles in a circle.

1. Since AB is the diameter of the circle, angle AOB is a right angle (90 degrees).

2. Angle AOC is given as 120 degrees.

3. Angle ACD is an inscribed angle that intercepts the same arc as angle AOC.

4. By the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc.

5. Therefore, the measure of arc AC is twice the measure of angle ACD.

6. Since angle AOC is 120 degrees, the measure of arc AC is also 120 degrees.

7. From step 5, we can conclude that the measure of angle ACD is half the measure of arc AC, which is 60 degrees.

Therefore, the measure of angle ACD is 60 degrees.