Final answer:
To find the measure of angle AOB, we can set up an equation based on the sum of the angles in a triangle. Solving for x, we find that the measure of angle AOB is 27 degrees.
Step-by-step explanation:
To find the measure of angle AOB, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees. Since B is in the interior of angle AOC, we can draw a triangle with vertex B and sides AO and CO. We are given that the measure of angle AOC is 108 degrees, so the sum of the measures of angle AOB and angle BOC is 180 - 108 = 72 degrees.
We are also given that the measure of angle AOC is 3 times the measure of angle AOB. So, we can set up the equation 3x + x + 72 = 180, where x represents the measure of angle AOB. Simplifying this equation, we get 4x + 72 = 180. Subtracting 72 from both sides, we get 4x = 108. Dividing both sides by 4, we get x = 27.
Therefore, the measure of angle AOB is 27 degrees.