Let's analyze the information in this problem.

Given Information:

1. AB is parallel to DEF: This suggests that we may need to use the concept of alternate interior angles.
2. Segments AE and BD intersect at C.
3. Angle B is 52°.
4. Angle CEF is 150°.

Objective:

We need to fill in the missing angles in the table. Let's go through each angle step by step.

Analyzing Each Angle:

1. Angle A: Since $AB \parallel DEF$ and $AE$ crosses both lines, angle $A$ should be an alternate interior angle with angle $CEF$, which measures 150°. Therefore, Angle A = 150°.

2. Angle B: This angle is given as 52°.

3. Angle BCA: This is the angle at point $C$ formed by lines $BC$ and $CA$. Since it forms part of the triangle $ABC$, we can use the interior angle sum property of triangles. The sum of angles in $\triangle ABC$ is 180°, so: $\text{Angle A} + \text{Angle B} + \text{Angle BCA} = 180°$ $150° + 52° + \text{Angle BCA} = 180°$ Solving for $\text{Angle BCA}$: $\text{Angle BCA} = 180° - 150° - 52° = -22°$