https://file.aiquickdraw.com/mathbot/file/1728523160086ywycsvz2.jpg

In the image, we see two intersecting lines forming four angles labeled \( \angle 1 \), \( \angle 2 \), \( \angle 3 \), and \( \angle 4 \). The text below the diagram indicates that it is incorrect to say \( \angle 1 \) and \( \angle 3 \) are a linear pair.

### Explanation:
A **linear pair** of angles are two adjacent angles that are on the same straight line, adding up to \( 180^\circ \). This means they must share a common side and their non-common sides form a straight line.

- **\( \angle 1 \) and \( \angle 3 \)** are opposite angles formed by two intersecting lines, which makes them **vertical angles**, not a linear pair. Vertical angles are congruent (equal in measure) but do not form a straight line together.
- Instead, \( \angle 1 \) and \( \angle 2 \), or \( \angle 3 \) and \( \angle 4 \), would be examples of linear pairs because they are adjacent angles that together form a straight line.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:
1. What is the difference between vertical angles and linear pairs?
2. How do you determine whether two angles form a linear pair?
3. Can vertical angles ever form a linear pair?
4. How do you prove that vertical angles are congruent?
5. Are there any other types of angle pairs formed by intersecting lines?

**Tip:** Always remember that linear pairs are adjacent and supplementary, meaning their sum is \( 180^\circ \).

Explore why angles 1 and 3 in the given diagram do not form a linear pair, with a detailed explanation of vertical angles and the linear pair theorem. Learn the difference between these types of angles and how they relate to intersecting lines, suitable for students in Grades 7-9.

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