In an isosceles trapezoid ABCD, the diagonal AC is the bisector of angle A and forms an angle

| September 9, 2021 | education

In an isosceles trapezoid ABCD, the diagonal AC is the bisector of angle A and forms an angle of 78 ° on the lateral side of CD. Find the corners of the trapezoid.

Since, by condition, AC is the bisector of the BAD angle, the angle BAC = CAD = BAD / 2.

Let the value of the angle BAC and CAD be equal to X0, then the angle BAD = 2 * BAC = 2 * X. Since the trapezoid is isosceles, the angle ADC = BAD = 2 * X0.

Angle ACB = CAD = X0, as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AC.

Then the angle ВСD = САВ + АСD = X + 78.

The sum of the angles of the trapezoid at the side is 180, then the angle BCD + ADC = (X + 78) + 2 * X = 180.

3 * X = 180 – 78 = 102.

X = 102/3 = 34.

Angle ADC = BAD = 2 * X = 68.

Angle BCD = ABC = X + 78 = 34 + 78 = 112.

Answer: The angles of the trapezoid are 680 and 112.



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