Straight through the top. angle C in triangle ABC, a straight line CK || AB is drawn; angle KCB = 42 °

Straight through the top. angle C in triangle ABC, a straight line CK || AB is drawn; angle KCB = 42 °. Find angles A and B in triangle ABC

We consider straight lines AB and CK, they are parallel by the condition of the problem. Line BC is a secant for these two lines.
The angles KСВ and ABC are cross-lying angles with parallel AB, СK and secant BC, we conclude:
∠KСВ = ∠ABC = 42 °.
Triangle ABC is rectangular, we find the second acute angle A:
∠ A = 90 ° – ∠ ABC = 90 ° – 42 ° = 48 °.
Answer: the degree measure of angle A is 48 °, angle B is 42 °.