In the parallelogram ABCD AB = 4, angle C = 60, point K is marked on the side BC so that KC

In the parallelogram ABCD AB = 4, angle C = 60, point K is marked on the side BC so that KC = 5 and angle BAK = 30 find AD.

Since the parallelogram has the same opposite angles, the angle BAD = BCD = 60.

The angle ВAK, by condition, is equal to 30, then the angle DAK = (60 – 30) = 30, which means that AK is the bisector of the angle BAD. Then the triangle AВK is isosceles, AB = BK = 4 cm.

The length of the side ВС = ВС + СK = 4 + 5 = 9 cm. Then АD = ВС = 9 cm, as opposite sides of the parallelogram.

Answer: The length of the side AD is 9 cm.