The OC beam divides the AOB angle in a ratio of 2: 9. Find the degree measure of the AOB

The OC beam divides the AOB angle in a ratio of 2: 9. Find the degree measure of the AOB angle if the AOC angle is 35 degrees less than the COB angle.

First of all, it should be noted that in this task there is a ratio (the angle is divided in a ratio of 2: 9). Therefore, we need to introduce the proportionality coefficient x. In this case, the AOC will be 2 * x and the COB will be 9 * x. Considering also that the difference between the angles is 35o, we will compose and solve the equation:
9 * x – 2 * x = 35;
7 * x = 35 | : 7;
x = 35/7;
x = 5o.
Determine the angles AOC and COB:
AOC = 2 * 5 = 10o;
COB = 9 * 5 = 45o.
Then the angle AOB is:
AOB = 10o + 45o = 55o.