Find the angles of an isosceles trapezoid if one of the sides is 7cm and the diagonal 7√3

Find the angles of an isosceles trapezoid if one of the sides is 7cm and the diagonal 7√3 makes an angle of 30 degrees with the base.

By the sine theorem CB / sin (BAC) = AC / sin (ABC)
sin (ABC) = AC * sin (BAC) / CB = 7 *√ (3) * sin (30) / 7 = root (3) / 2
Angle ABC = 60
Angle BAD = angle ABC as the trapezoid is isosceles
Angle BCD = 180 – Angle ABC = 120
Angle ADC = angle BCD as the trapezoid is isosceles

Answer: The angles between the sides of the trapezoid and the lower base are 60 degrees, the angles between the sides of the trapezoid and the upper base are 120 degrees.