Parallelogram ABCD. The bisectors of angles A and D intersect at point K on the BC side. The side is 40. You need to find the sun.
Since AK is the bisector of the angle BAD, the angle ABK = DAK.
In a parallelogram, the opposite sides are parallel, then the angle AKВ = DAK as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AK.
Then in the triangle ABK the angle BAK = BKA, and then the triangle ABK is isosceles with the base AK.
Then BK = AB = 40 cm.
Similarly, the triangle CDK is isosceles, CK = CD = 40 cm.
Then BC = BK + СK = 40 + 40 = 80 cm.
Answer: The length of the BC side is 80 cm.
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