Lines AB and BC are perpendicular. The BK beam divides the angle into two angles, one of which is 2/3

Lines AB and BC are perpendicular. The BK beam divides the angle into two angles, one of which is 2/3 of the other. Find these corners.

Given:
straight lines AB and BC are perpendicular,
ray BK divides the angle into two angles,
angle ABK = 2/3 * angle KВС.
Find the degree measures of the angles ABK and KBC -?
Decision:
Angle ABC is straight, since straight lines AB and BC are perpendicular.
Let the KBC angle = x degrees, then the AВK angle = 2/3 * x degrees. We know that the degree measures of the right angle is 90 degrees. Let’s make the equation:
2/3 * x + x = 90;
x * (2/3 + 1) = 90;
x * 5/3 = 90
x = 90: 5/3;
x = 90 * 3/5;
x = (90 * 3) / 5;
x = (18 * 3) / 1;
x = 54 degrees – the degree measure of the KBC angle;
90 – 54 = 36 degrees – the degree measure of the ABK angle.
Answer: 54 degrees; 36 degrees.