The height BK of the parallelogram ABCD divides its side AD into segments AK and KD such, AK = 4 cm, KD = 6 cm.Find the angles and perimeter of the parallelogram if the angle ABK = 30 degrees
1. The length of the leg of the AK, located opposite the angle of 30 °, is equal to 1/2 the length of the hypotenuse AB. Taking this into account, we calculate the length of the side AB, which is the hypotenuse in the AВK triangle.
AB = 2 x AK = 2 x 4 = 8 cm.
2. AD = AK + DK = 4 + 6 = 10 cm.
3. Opposite sides and angles of a parallelogram are equal:
AB = CD = 8 cm.
BC = AD = 10 cm.
Angle A = angle C = 180 ° – 30 ° – 90 = 60 °.
Angle B = angle D = 90 ° + 30 ° = 120 °.
4. The total length of all sides of the parallelogram (perimeter) is 2 AB + 2 BC = 2 x 8 + 2 x
10 = 36 cm.
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