In the parallelogram ABCD, from the vertex B of the obtuse angle, the perpendicular BK

| April 28, 2021 | education

In the parallelogram ABCD, from the vertex B of the obtuse angle, the perpendicular BK is lowered to the side AD, AK = BK. Find the angles of a parallelogram

First, let’s write down what is given.
Given: ABCD – parallelogram; ВK perpendicular to the AD side; AK = BK.
Find: angles of a parallelogram.
Decision:
Let’s construct a parallelogram ABCD with an obtuse angle B and draw a perpendicular ВC.
Since ВK is a perpendicular, the angle AKВ = angle ВKD = 90 °.
The AKВ triangle is rectangular. But since AK = ВK, the AKВ triangle is also isosceles. Hence, the angle AВK = angle KAВ = (180 ° – 90 °) / 2 = 45 °.
Angle A = angle C = 45 ° – by the property of a parallelogram.
Angle B = angle D = 180 ° – 45 ° = 135 ° – by the property of a parallelogram.
Answer: 45 °; 45 °; 135 °; 135 °.



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