Find the angle of an isosceles trapezoid ABCD if the diagonal AC forms angles equal to 30 degrees

univerkov | March 3, 2021 | education

Find the angle of an isosceles trapezoid ABCD if the diagonal AC forms angles equal to 30 degrees and 105 degrees with the base BC and the lateral side CD.

Determine the value of the angle ВСD.

Angle BCD = BCA + DCA = 30 + 105 = 135.

In a trapezoid, the sum of the angles at the lateral side is 180, then the angle ADC = (180 – BCD) = (180 – 135) = 45.

Since the trapezium ABCD is isosceles, its angles at the base are equal, then the angle ABC = BCD = 135, the angle BAD = ADC = 45.

Answer: The angles of the trapezoid are 45, 135, 45, 135.

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