Youin the adjoining figure there is a circle with center O. If DC, diameter AB and m less than AOC=120 degree, then M less than ACD is?

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

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

2. Angle AOC is given as 120 degrees.

3. Angle AOB and angle AOC are both angles that intercept the same arc AC. According to the inscribed angle theorem, these angles are equal in measure.

4. Therefore, angle AOB = angle AOC = 120 degrees.

5. Angle MCD is an inscribed angle that intercepts the same arc AC as angle AOC.

6. By the inscribed angle theorem, angle MCD has half the measure of the intercepted arc.

7. Since angle AOC is 120 degrees, the intercepted arc AC is also 120 degrees.

8. Therefore, angle MCD = 1/2 * 120 degrees = 60 degrees.

So, the measure of angle MCD is 60 degrees.