Luz OC passes between the sides of the angle AOB equal to 140 degrees.

Luz OC passes between the sides of the angle AOB equal to 140 degrees. Find the AOC and COB angles if the AOC angle is 50 degrees greater than the COB angle.

Since the AOC angle is 50 degrees greater than the CОВ angle, we express the value of the AOC angle:
AOC angle = CОВ angle + 50 degrees
According to the condition, the angle AOB = 140 degrees, then the angle АОС + angle CОВ = angle AOB = 140 degrees Substitute in the expression the value of the AOC angle, which we expressed through the COB angle:
COB angle + 50 degrees + COB angle = 140 degrees;
2 COB angle = 140 degrees – 50 degrees;
2 COB angle = 90 degrees;
COB angle = 90 degrees / 2;
CОВ angle = 45 degrees.
Find the angle AOC:
AOC angle = AOB angle – AOC angle;
angle AOC = 140 degrees – 45 degrees;
angle AOC = 95 degrees.
Answer: AOC angle = 95 degrees, COB angle = 45 degrees.