The OC beam divides the unfolded angle AOB into two angles AOC and BOC, so that the AOC angle

The OC beam divides the unfolded angle AOB into two angles AOC and BOC, so that the AOC angle is 30 degrees greater than the BOC angle. Find AOC and BOC.

1. By the condition of the problem, it is known that the unfolded angle AOB is divided into angles AOC and BOC, while the first is 30 ° more than the second.

2. Let’s designate the angle BOC as x °, then the angle AOC = (x + 30) °.

Since the unfolded angle is 180 °, we write and solve the equation:

x + (x + 30) = 180 °, that is, 2 x = 180 ° – 30 ° = 150 °, whence x = 150 °: 2 = 75 °.

Let’s calculate the value of the larger angle:

75 ° + 30 ° = 105 °.

Answer: Angle AOC is 75 °, BOC is 105 °.