Find CD.

This problem involves a triangle ACD with a right angle at C. We are given AD = 20. We are also given a point B on CD such that ∠ABC = 150°.

To find CD, we need more information, such as the length of AC, or angles within triangle ACD or related triangles.

Let's consider the triangle ABC. We know ∠ACB = 90°.

If we knew AC, we could find BC using trigonometry if we knew ∠BAC or ∠ABC. However, ∠ABC is external to triangle ACD.

Let's consider the given angle ∠ABC = 150°. This is an exterior angle to triangle ABD. If we knew ∠CBD, then ∠ABC + ∠CBD = 180°, so ∠CBD = 180° - 150° = 30°.

In right-angled triangle ACD, we have AC² + CD² = AD² = 20² = 400.

If we consider triangle ABC, we have AC² + BC² = AB².

We need more information to solve for CD.

Answer: Insufficient information to determine CD.