Diagonal BD of trapezoid ABCD is perpendicular to the base, angle ABD = 37
| June 22, 2021 | education
Diagonal BD of trapezoid ABCD is perpendicular to the base, angle ABD = 37 degrees, angle CDB = 64 degrees. Calculate the angles of the trapezoid.
Since the diagonal BD is perpendicular to the bases of the trapezoid, it divides the trapezoid into two right-angled triangles, ABD and CBD.
In a right-angled triangle ABD, the angle BAD = (180 – ADB – ABD) = 180 – 90 – 37 = 53.
In a trapezoid, the sum of the angles at its lateral side is 180, then the angle ABC = (180 – BAD) = 180 – 53 = 127.
In a right-angled triangle ВСD, the angle ВСD = (180 – CBD – СDВ) = 180 – 90 – 64 = 26.
Angle ADC = 90 + 64 = 154.
Answer: The angles of the trapezoid are 53, 127, 26, 154.
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