In a rectangular trapezoid ABCD with bases AD and BC, the diagonal AC is the bisector

In a rectangular trapezoid ABCD with bases AD and BC, the diagonal AC is the bisector of the acute angle A. Find the angle ACD if the angle ABC = 144 degrees.

Since AC is the bisector of the BAD angle, the BAC angle is equal to the BCA angle. The BCA angle is equal to the CAD angle as criss-crossing angles at the intersection of parallel straight lines BC and AD of the secant AC. Then the angle ABC is equal to the angle of the BCA, and therefore the triangle ABC is isosceles.

Then the angle BAC = BAC = (180 – ABC) / 2 = (180 – 144) / 2 = 36/2 = 18.

Then the angle ACD = BCD – BCA = 90 – 18 = 62.

Answer: Angle ACD is 62.