Given: triangle ABC, Angle C = 90 degrees, AC // BK, Angle ABK = 60 degrees, Find: Angle A and Angle ABC

In the condition, we are given a triangle ABC, it is also known that the angle C = 90 °, line AC parallel to line BK, angle ABK = 60 °.

We need to find the degree measure of the angles A and ABC.

Since the AC side of the triangle is parallel to BK, AB is a secant.

From this we conclude that the angle ABK is equal to the angle A, as cross-lying.

So, according to the theorem on the sum of the angles of a triangle (180 °), we can find the angle:

angle ABC = 180 ° – 60 ° – 90 ° = 30 °.

Then the degree measure of the angle A = 180 ° – 90 ° – 30 ° = 60 °.

Answer: angle A = 60 °; angle ABC = 30 °.



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