Math Problem Statement

Which of these angles are linear pairs?

Solution

In the new diagram, the angles 1 through 5 are formed by the intersection of lines ll, mm, and nn.

To identify linear pairs, recall that they consist of two adjacent angles whose non-common sides form a straight line (i.e., their sum is 180 degrees).

Linear Pairs in the Diagram:

  • Angles 1 and 2: They are adjacent and together form a straight line along line ll. Thus, they are a linear pair.
  • Angles 2 and 3: These angles are adjacent and form a straight line along line nn. Therefore, they are a linear pair.
  • Angles 3 and 4: These angles are adjacent and form a straight line along line ll. Hence, they are a linear pair.
  • Angles 4 and 5: These angles are adjacent and form a straight line along line mm. Therefore, they are a linear pair.

Summary:

  • Linear Pairs:
    • Angles 1 and 2
    • Angles 2 and 3
    • Angles 3 and 4
    • Angles 4 and 5

Do you have any further questions or need more details?

Here are some related questions:

  1. How does the concept of supplementary angles relate to linear pairs?
  2. Can three angles form a linear pair? Why or why not?
  3. If angle 2 is 70 degrees, what is the measure of angle 1?
  4. How do linear pairs differ from vertically opposite angles?
  5. Can angles 1 and 3 ever form a linear pair?

Tip: Linear pairs are always adjacent and share a common side. Identifying the straight line they form can help determine if they are a linear pair.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles

Formulas

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Theorems

Linear pairs of angles

Suitable Grade Level

Grades 6-8