In a trapezoid, the sides are equal to the smaller base. The diagonal makes an angle

In a trapezoid, the sides are equal to the smaller base. The diagonal makes an angle with the base of 30 degrees. Find the obtuse angle at the base of the trapezoid.

Since, according to the condition, AB = BC = CD, then the triangle ABC is isosceles, and therefore the angle BAC = BCA.

Angle BCA = CAD = 30, as criss-crossing angles at the intersection of parallel lines AD and BC secant AC.

Then the angle BAC = CAD = 30, and the angle BAD = BAC + CAD = 30 + 30 = 60.

The sum of the angles of the trapezoid with its lateral side is 180, then the angle ABC = 180 – 60 = 120.

Angle BCD = ABC = 120.

Answer: The obtuse angle of the trapezoid is 120.