Adjacent angles BOA and COA are ratios 4: 5, OM is the bisector of AOC. Find the corner of the BOM.

1. Since the angle BOA and the angle СOA are adjacent, their sum will be equal to 180 degrees. Let x be the coefficient of proportionality, then the angle BOA = 4x, the angle COA = 5x:
4x + 5x = 180 degrees; 9x = 180 degrees; x = 20 degrees.
It turns out that the angle BOA = 4x = 4 * 20 = 80 (degrees), the angle СOA = 5x = 5 * 20 = 100 (degrees).
2. The bisector divides the angle in half, so the angle AOM = angle MOC = angle SOA / 2 = 100/2 = 50 (degrees).
3. Find the PTO angle:
PTO angle = BOA angle + AOM angle;
PTO angle = 80 + 50 = 130 (degrees).
Answer: PTO angle = 130 degrees.