Final answer:
The measure of angle AOB is 42 degrees.
Step-by-step explanation:
To find the measure of angle AOB, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Since O is the center of the circle, angle BOC is a central angle, and its measure is equal to twice the measure of the inscribed angle AOB. Therefore, AOB = BOC ÷ 2. Given that BOC = 84 degrees, we can calculate AOB as follows:
AOB = 84 ÷ 2 = 42 degrees.