Given that the problem involves three parallel lines cut by a transversal, we can use the properties of parallel lines and transversals to find the measure of angle 7.

Step 1: Understanding the Relationship of Angles

Parallel lines cut by a transversal form several types of angle pairs:

1. Corresponding angles: These angles are equal.
2. Alternate interior angles: These angles are also equal.
3. Same-side interior angles (consecutive interior angles): These angles are supplementary (sum to 180°).

Step 2: Identify the Angle Relationships

• Angle 4 is given as $132^\circ$.
• Angle 7 corresponds to Angle 4 since they are both on the same relative side of their respective intersections and are corresponding angles.

Step 3: Apply the Corresponding Angles Theorem

Since Angle 7 and Angle 4 are corresponding angles, they must be equal: $\text{Angle 7} = \text{Angle 4} = 132^\circ$

Final Answer:

The measure of Angle 7 is $\boxed{132^\circ}$.

Would you like more details or have any questions about this solution?

Here are five related questions to expand the understanding:

1. What are alternate interior angles, and how do they relate to transversals?
2. How can you use the consecutive interior angles theorem with a transversal?
3. If angle 6 is 48°, what would be the measure of angle 8?
4. What is the sum of the angles on one side of a transversal between two parallel lines?
5. Can a transversal form supplementary angles that are not on the same side of the transversal?

Tip: Remember, corresponding angles formed by a transversal with parallel lines are always equal, making this property very useful in geometry problems!