The OC beam c divides the right angle AOB so that the AOC angle is 45 ° less than the BOC angle. Find the BOC value.

According to the condition of the problem, the sum of the degree measures of the AOC and AOC angles is 90 °, and the difference in the degree measures of the AOC and AOC angles is 45 °:

∠AOС + ∠ВOС = 90 °;

∠ВOС – AOС = 45 °;

We add the left and right sides of the equations and find from the resulting equation the value of the ВOС angle:

∠AOС + ∠ВOС + ∠ВOС – AOС = 90 ° + 45 °;

2∠ВOС = 135 °;

∠ВOС = 67.5 °.

Answer: 67.5 °.