ABCD – isosceles trapezoid. AB = BC = CD, angle ACD = 90 degrees. Find all corners.

| April 11, 2021 | education

Since, according to the condition, AB = BC, the triangle ABC is isosceles, therefore the angles BAC and BCA are equal to each other, as are the angles at the base of an isosceles triangle.

Let us consider the angles BCA and CAD, which are also equal as they lie crosswise at the intersection of parallel straight lines AD and BC of the secant AC. Then the angle BAC = BAC = CAD.

Angle BCD = BCA + ACD = BCA + 90.

Let the angles BAC, BCA and CAD be equal to X.

The sum of the opposite angles of the trapezoid is 180.

Then 180 = X + X + X + 90.

3 * X = 180 – 90 = 90.

X = 90/3 = 30.

Then the angle BAD = BAC + CAD = 60.

Angle BCD = BCA + ACD = 30 + 90 = 120.

Since, by condition, the trapezoid is isosceles, the angles at the base are equal. BAD = CDA = 60,

ABC = BCD = 120.

Answer: BAD = CDA = 60, ABC = BCD = 120.



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