Since angle AOC is 85 degrees, angle BOC is 95 degrees. Since angles AOB and BOC are supplementary, angle AOB is 115.32 degrees. Thus, the correct option is A.
Since angle AOC is 85 degrees, angle AOC + angle BOC = 180 degrees, so angle BOC is 180 - 85 = 95 degrees.
Since angle AOB and angle BOC are supplementary angles, angle AOB + angle BOC = 180 degrees.
We are also given that angle AOB = 4x - 15 and angle BOC = 2x + 10.
Substituting these values into the equation above, we get:
(4x - 15) + (2x + 10) = 180
Combining like terms, we get:
6x - 5 = 180
Adding 5 to both sides, we get:
6x = 185
Dividing both sides by 6, we get:
x = 30.83
Substituting this value into the equations for angle AOB and angle BOC, we get:
angle AOB = 4(30.83) - 15 = 115.32 degrees
angle BOC = 2(30.83) + 10 = 72.66 degrees
Therefore, the degree measures of angle BOC and angle AOB are 72.66 degrees and 115.32 degrees, respectively.
So, the correct option is A: m= 30°; m= 55°.