Since the segment MN is the diameter of the circle, the arc MACN has an angle with a measure of 180°, Then by adding the measures of the angles of the arcs MA, AC and CN we should get 180°, like this:
mMA + mAC + mCN = 180
By replacing 55° for mMA and 65° for mCN, we can solve for mAC to get:
55 + mAC + 65 = 180
120 + mAC = 180
120 - 120 + mAC = 180 - 120
mAC = 60
The measure of the arc ACN is calculated by adding the measures of the angles AC and CN, then we get:
mACN = mAC + mCN
mAC = 60 + 65
mAC = 125
Then, the angle of ACN has a measure of 125°
