In the parallelogram ABCD LB = 140 °. Point F lies on the side BC, with LADF = 70 °, BF = 5 cm. AD = 20 cm. Find AB.

univerkov | March 26, 2021 | education

In a parallelogram, opposite angles are equal, then the angle ABC = ADC = 140.

Determine the value of the angle CDF, CDF = ADC – ADF = 140 – 70 = 70.

Angle CFD = ADF = 70, since they are criss-crossing angles at the intersection of parallel lines AD and BC of the secant DF. Therefore, triangle FCD is isosceles, CF = CD.

Since the opposite sides of the parallelogram are equal, AD = BC, then CF = CD = BC – BF = 20 – 5 = 15 cm.

AB = CD = 15 cm.

Answer: Side AB = 15 cm.

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