Final answer:
Given that m1 + m2 equals 180 degrees and the total of all central angles in a circle is 360 degrees, the measure of the third angle would also be 180 degrees. This is because all central angles must add up to 360 degrees.
Step-by-step explanation:
The question involves finding the measure of an unknown central angle in a circle, given the sum of two other central angles. If we know that the sum of all central angles in a circle is 360 degrees and m1 + m2 = 180 degrees, then the remaining angle, m3, would also be 180 degrees, because m1 + m2 + m3 must total 360 degrees. This is in line with the basic property of circles where the central angles sum up to 360 degrees. The example provided would be better understood if one visualizes a triangle within a circle, where each vertex of the triangle touches the circumference and the angles at the vertices form the central angles of the segments of the circle.