Through the vertex of the right angle C of the triangle ABC, a straight line CD is drawn, parallel

Through the vertex of the right angle C of the triangle ABC, a straight line CD is drawn, parallel to the side AB. Find the angles A and B if the angle DCB = 37 degrees.

Line CB intersects two parallel lines AB and CD and is a secant for them. The angle DCB and the angle ABC are equal to each other, since they are intersecting. The value of the angle DСВ = 37 degrees according to the condition of the problem, therefore the angle ABC = 37 degrees. This is corner B of our triangle.
The angles of any triangle add up to 180 degrees. Our triangle is rectangular, angle C = 90 degrees.
A + B + C = 180,
C = 90, and B = 37
from here we find the value of the angle A
A = 180-90-37
A = 43
Answer: A = 43, B = 37 degrees