In a rectangular trapezoid, the angle and the angle that makes up the smaller diagonal with the smaller base

In a rectangular trapezoid, the angle and the angle that makes up the smaller diagonal with the smaller base are 60 degrees each. find the midline of the trapezoid if the larger base is 12?

In the trapezoid ABCD, the angle BCA = CAD as the cross-lying angles at the intersection of parallel straight lines BC and AD of the secant AD. Angle CAD = BCA = 60. Then triangle ACD is equilateral, since the angles at its base AD are 60, and therefore AC = CD = AD = 12 cm.

In a right-angled triangle ABC, the angle BAC = (180 – 60) = 30, then the leg BC = AC / 2 = 12/2 = 6 cm.

Determine the length of the midline of the trapezoid.

KM = (BC + AD) / 2 = (6 + 12) / 2 = 9 cm.

Answer: The length of the middle line of the trapezoid is 9 cm.