Math Problem Statement
Solution
In the image, we see two intersecting lines forming four angles labeled , , , and . The text below the diagram indicates that it is incorrect to say and are a linear pair.
Explanation:
A linear pair of angles are two adjacent angles that are on the same straight line, adding up to . This means they must share a common side and their non-common sides form a straight line.
- and 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, and , or and , 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:
- What is the difference between vertical angles and linear pairs?
- How do you determine whether two angles form a linear pair?
- Can vertical angles ever form a linear pair?
- How do you prove that vertical angles are congruent?
- 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 .
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Math Problem Analysis
Mathematical Concepts
Linear Pair
Vertical Angles
Intersecting Lines
Angle Relationships
Formulas
-
Theorems
Linear Pair Theorem
Vertical Angles Theorem
Suitable Grade Level
Grades 7-9
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