Lines AB and BC are perpendicular. Beam BD divides angle ABC into two angles, one of which is two-thirds of the other. Find these corners.
Since, according to the condition of the problem, lines AB and BC are perpendicular, it means that the angle ABC formed by straight lines AB and BC is a straight line and is equal to 90 degrees.
Let the ABD angle be x degrees, then the CBD angle will be (2x / 3) degrees. Since, according to the condition of the problem, the BD beam divides the angle ABC into two angles, then:
angle ABD + angle CBD = angle ABC;
x + 2x / 3 = 90;
(3x + 2x) / 3 = 90;
5x / 3 = 90;
5x = 90 * 3;
5x = 270;
x = 270: 5;
x = 54 (degrees)
If x = 54, then 2x / 3 = 2 * 54/3 = 2 * 18 = 36 (degrees).
Answer: 54 degrees and 36 degrees.
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