∠AOB- deployed. The OC beam divides ∠AOB in a ratio of 1: 5, and the OM beam divides the bisector COB. Find ∠AOM.

1) Find the angles AOC and BOC.

Because angles AOC and BOC are 1: 5, then we take one part as x. Let the AOC angle be x, then the AOC angle is 5x. The sum of these angles is equal to the value of the angle AOB (unfolded angle is 180 degrees) or (x + 5x) degrees or 180 degrees.

x + 5x = 180;

6x = 180;

x = 180: 6;

x = 30 – angle BОС;

5x = 30 * 5 = 150 – AOC angle.

2) Because OM is the bisector of the angle BOC (the bisector divides the angle in half), then the angle BOM = angle COM = 30: 2 = 15.

3) AOM angle = AOC angle + COM angle;

angle AOM = 150 + 15 = 165.

Answer. 165.