Through the vertex B of the triangle ABC, draw a straight line MK parallel to the straight line AC Angle MBA

Through the vertex B of the triangle ABC, draw a straight line MK parallel to the straight line AC Angle MBA = 42 degrees Angle CBK = 56 degrees Find the angles of triangle ABC.

The angle BAC is equal to the angle MBA as criss-crossing angles at the intersection of parallel straight lines MK and AC secant AB. Angle BAC = 42.

The ACB angle is equal to the СBК angle as the criss-crossing angles at the intersection of parallel lines MK and AC secant BC. Angle АСВ = 56.

Then the angle ABC = 180 – BAC – ABC = 180 – 42 – 56 = 82.

Answer: The angles of the triangle are 42, 56, 82.