The diagram below shows several parking spots near the grocery store, formed with three parallel line segments and a transversal.

3 parallel lines are cut by a transversal to form 3 sets of 4 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12.

If the measure of angle 4 is 132°, what is the measure of angle 7?
32°
48°
132°
148°

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!

3 parallel lines are cut by a transversal to form 3 sets of 4 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12. If the measure of angle 4 is 132°, what is the measure of angle 7? 32°, 48°, 132°, 148°.

In this geometry problem, learn how to find the measure of angle 7 using the Corresponding Angles Theorem. With three parallel lines cut by a transversal, this question explores key concepts like corresponding and supplementary angles. Suitable for students in Grades 8-10.

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