The bisectors of angles A and D of the ABCD parallelogram intersect at point M, which lies on the BC side. Find BC if AB = 40.

Since ABCD is a parallelogram, its opposite sides are equal and parallel.

Then the angle АМВ = DAM as criss-crossing angles at the intersection of parallel straight lines АD and ВС secant АМ.

Then in the triangle ABM the angle BAM = BMA, which means that the triangle ABM is isosceles, BM = AB = 40 cm.

Similarly, the CDM triangle is isosceles, CD = CM = 40 cm.

Then BC = AM + CM = 40 + 40 = 80 cm.

Answer: The length of the BC side is 80 cm.