In trapezoid ABCD, it is known that AB is parallel to AD, AB is perpendicular to AD
| April 24, 2021 | education
In trapezoid ABCD, it is known that AB is parallel to AD, AB is perpendicular to AD, BC is equal to CD, angle ABD = 80 degrees. Find the corners of the trapezoid.
Since, by condition, ВС = СD, then the triangle ВСD is isosceles, and therefore the angle СD = СDВ.
Angle CBD = ABC – ABD = 90 – 80 = 10.
The angle CBD = CDB = 10, then the angle BCD = 180 – 10 – 10 = 160.
In a trapezoid, the sum of the angles adjacent to the lateral side is 180.
Angle ВСD + АDC = 180, then АDC = 180 – 160 = 20.
Answer: The angles of the trapezoid are 90, 90, 160, 20.
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