Let's analyze the problem in detail.

1. Transformation of Triangle ABC:
   • The triangle is reflected across the y-axis.
   • It is rotated by 30° about the origin.
   • It is translated 7 units to the left.

These transformations will affect the orientation and position of triangle ABC, but not its size or shape.

2. Perimeter Comparison:

   • A reflection, rotation, and translation are rigid transformations. They do not change the size of the figure, which means the perimeter of triangle A'B'C' will be equal to the perimeter of triangle ABC.
   • So, CHOICE 1 should be "equal to."

3. Angle Comparison:

   • The second question asks about the angles after transformation. Since rigid transformations preserve angle measures, the angle corresponding to angle CAB in the transformed triangle will be the one with the same relative position.
   • After reflecting across the y-axis and rotating 30°, the vertices are relabeled, so we must find which angle corresponds to angle CAB. This depends on the order of vertices after the transformation.

   Considering the transformations, the measure of angle CAB will now correspond to angle C'A'B' in the new triangle.

Thus, CHOICE 2 is "C'A'B'."

Summary:

• CHOICE 1: equal to
• CHOICE 2: C'A'B'

Would you like further explanation on any step, or do you have any additional questions?

Here are 5 related questions:

1. How do rigid transformations preserve the properties of geometric shapes?
2. What happens to the orientation of a shape after reflection across the y-axis?
3. Can non-rigid transformations change the perimeter of a shape? Give examples.
4. How does rotating a shape around a point affect its angles?
5. What is the effect of translations on the distance between points in a shape?

Tip: Rigid transformations like reflection, rotation, and translation do not alter the size or shape of geometric figures, preserving both angles and side lengths.