In an isosceles trapezoid, the smaller base is equal to the lateral side and the larger

| June 1, 2021 | education

In an isosceles trapezoid, the smaller base is equal to the lateral side and the larger base is equal to the diagonal. Calculate the angles of the trapezoid.

Let us denote the trapezium ABCD, where the lateral sides AB = CD, and are equal to the smaller side BC. Diagonal AC = AD. Let the angles at the base of the triangle <BAC = <BCA = x.
and in the triangle ACD of the angle at the base of CD: <ACD = <ADC = y.
Now let’s compose different equalities for the angles, taking into account that the sum of the one-sided angles in the trapezoid = 180 degrees. In the triangle ACD, the following angles are: x, y, y.
In triangle ABC the angles are x, x, and 180-2x.
Equalities: 2y + x = 180. (the sum of one-sided angles), 2x = y (as the same angles at the base of a trapezoid. Hence: 2y + x = 4x + x = 5x = 180, x = 36, y = 72.
Trapezium angles: 72.72, and 108, 108.



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