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In this figure, we have two sets of intersecting lines at points where angles are formed. Let's name the linear pairs and vertical angles accordingly:

### 1. **Linear Pairs of Angles:**
Linear pairs are adjacent angles that form a straight line. From the figure, the linear pairs are:

- \( \angle a \) and \( \angle b \) (since they are adjacent and along the same line at point \( c \)).
- \( \angle c \) and \( \angle d \) (since they form a linear pair at point \( c \)).
- \( \angle e \) and \( \angle f \) (since they form a linear pair at point \( e \)).
- \( \angle g \) and \( \angle h \) (they form a linear pair at point \( g \)).

### 2. **Vertical Angles:**
Vertical angles are opposite angles formed by two intersecting lines. The pairs of vertical angles are:

- \( \angle a \) and \( \angle c \) (they are opposite each other at point \( c \)).
- \( \angle b \) and \( \angle d \) (opposite angles at point \( c \)).
- \( \angle e \) and \( \angle g \) (opposite at point \( e \)).
- \( \angle f \) and \( \angle h \) (opposite angles at point \( e \)).

Would you like further details on how these angles relate or more explanation on any specific concept?

### Here are 5 related questions to explore:
1. What is the property of vertical angles regarding their measures?
2. Can a linear pair of angles ever be complementary?
3. What is the sum of the measures of a linear pair of angles?
4. How do alternate interior angles relate to vertical angles in parallel line scenarios?
5. How can you determine if two lines are parallel based on angle relationships at a transversal?

**Tip:** Vertical angles are always congruent (equal in measure).

In the given figure, name each linear pair of angles and pair of vertical angles.

Learn how to identify and name linear pairs and vertical angles in a given geometrical figure. This problem covers key concepts in geometry, including the Linear Pair Theorem and the Vertical Angles Theorem, suitable for middle school students in Grades 6-8.

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