Given a trapezoid ABCD, the height of which is 6 cm, the angle A is 45 degrees. Find the angle CD-?

The sum of the inner angles of a trapezoid is 360 degrees. The drawn height, from apex B to the base AD of the trapezoid, forms a right-angled triangle whose interior angles add up to 180 degrees.

The drawn height, from apex B to the base AD of the trapezoid, also divides the inner corner B into two angles, 45 and 90 degrees.

As a result, we have ∠A = 45; ∠B = 45 + 90; ∠C? ∠D = 30.

If the height dropped from the vertex C is denoted by H, then from the triangle HСD we have that ∠HСD = 90 – 30 = 60 degrees.

∠A + ∠B + ∠C + ∠D = 360; => ∠C = 360 – 45 – 135 – 30 = 360 – 210 = 140.

Answer: ∠C = 140 °.