In an isosceles trapezoid ABCD with bases AD and BC, the angle BDA = 45 degrees and the angle BDC

In an isosceles trapezoid ABCD with bases AD and BC, the angle BDA = 45 degrees and the angle BDC = 43 degrees. Find the degree measure of the angle ABD.

Since the trapezoid is isosceles, the BAD angle at its base is equal to the CDA angle. The angle CDA is defined as the sum of the angles BDA and BDC: 45+ 43 = 88 degrees. Since the sum of the interior angles of any triangle is 180 degrees, the angle ABD in triangle ABD will be 180 – (88 + 45) = 47 degrees.