In the parallelogram ABCD, the beam BK is the bisector ∠ ABC. Find the angles of the parallelogram ABCD, if ∠ ВКА = 34 °.

univerkov | February 10, 2021 | education

Angle AKВ = KВС as criss-crossing angles at the intersection of parallel straight lines AD and BC secant ВK. Since ВK is the bisector of angle ABC, then the angle ABC = KBC = 34. Then the angle ABC = AВK + KBC = 34 + 34 = 68.

Since the sum of the angles in the AВK triangle is 180, the angle ВAK = 180 – 34 – 34 = 112.

Answer: The angles of the parallelogram AВСD are equal to 68 and 112 degrees.

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