Math Problem Statement

Are angles 1 and 3 a linear pair?

Solution

In the image, we see two intersecting lines forming four angles labeled 1\angle 1, 2\angle 2, 3\angle 3, and 4\angle 4. The text below the diagram indicates that it is incorrect to say 1\angle 1 and 3\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 180180^\circ. This means they must share a common side and their non-common sides form a straight line.

  • 1\angle 1 and 3\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, 1\angle 1 and 2\angle 2, or 3\angle 3 and 4\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 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Linear Pair
Vertical Angles
Intersecting Lines
Angle Relationships

Formulas

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Theorems

Linear Pair Theorem
Vertical Angles Theorem

Suitable Grade Level

Grades 7-9