Find the angle ACD of a rectangular trapezoid ABCD if the acute angle D of the trapezoid

Find the angle ACD of a rectangular trapezoid ABCD if the acute angle D of the trapezoid is 30 and the diagonal AC makes an angle of 20 with the lateral side AB.

Since the trapezoid is rectangular, the angle BAD = ABC = 90.

Then the angle CAD = (BAD – BAC) = (90 – 20) = 70.

Consider triangle ACD. The sum of the interior angles of a triangle is 180, then:

Angle ACD = (180 – CAD – ADC) = (180 – 70 – 30) = 100.

Answer: The angle ACD is 100.