In the parallelogram ABCD, the angle is 30 degrees Find the other angles

In the parallelogram ABCD, the angle is 30 degrees Find the other angles and sides of the parallelogram knowing that the side AB is 5 cm and the perimeter is 20 cm

The solution of the problem:

Angle A = angle C = 30 °.

Angle B = Angle D = 180 ° – 30 ° = 150 °

1. Let’s define the sides of the parallelogram AD and BC.

P = 2AB + 2AD;

2AD = P – 2AB;

AD = (P – 2AB): 2;

AD = (20 – 2 * 5): 2;

AD = 10: 2;

AD = 5 cm.

ВС = АD = 5 cm.

Answer: the side of the parallelogram is 5 cm and the angles are 30 ° and 150 °.