Final answer:
The statement is true; if angle AOB is a straight angle, then angle AOC plus angle COB indeed equals 180 degrees since they are adjacent angles forming a line.
Step-by-step explanation:
The statement is true. If angle AOB is a straight angle, it measures 180 degrees since a straight angle is defined as an angle that is straight or 180 degrees by definition. Given that point C is not on the line AB, angle AOC and angle COB lie in the same plane and share a common ray OC.
When two angles lie within the same plane and share a common ray and their non-common sides form a straight line, the sum of their measures is 180 degrees. Hence, if angle AOC and angle COB are adjacent to each other and their non-common sides form line AB, then angle AOC + angle COB equals 180 degrees.