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

In parallelogram ABCD, AB = 4cm, angle C = 60 degrees, point K is marked on side BC, so KC = 5cm, angle BAK = 30 degrees. Find the length of side AD.

1. Let us denote the angle by the symbol ∠.

2. ∠А = ∠С, since the angles opposite each other are equal. ∠А = 60 °.

3. ∠DAK = ∠A – ∠BAK = 60 ° – 30 ° = 30 °.

4. AK is a bisector, since it divides ∠A into two equal angles: ∠DAK = BAK = 30 °.

5. According to the properties of the parallelogram, the bisector AK separates the isosceles triangle ABK from the parallelogram.

Therefore, BK = AB = 4 cm.

6. BC = СK + BK = 5 + 4 = 9 cm.

7. In a parallelogram, the opposite sides are equal:

AD = BC = 9 cm.

Answer: AD = 9 cm.