LINEAR PAIR
Definition Of Linear Pair
Linear Pair is a pair of adjacent angles that form a straight line.
More About Linear Pair
The sum of the measure of the angles in a linear pair is supplementary or 180°.
If one angle of a linear pair is acute (below 90°), then the other angle is obtuse (above 90°).
Example of Linear Pair
In the above figure, ∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, and ∠4 and ∠1 are linear pairs, as any pair of these angles forms a straight line.
Video Examples: Linear Pairs and Vertical Angles
Solved Example on Linear Pair
Ques: If m∠CAB = 32, then find the m∠CAD in the figure shown.
Choices:
A. 148
B. 212
C. 158
D. 32
Correct Answer: A
Solution:
Step 1: If ∠DAB is a straight angle, then m∠CAD + m∠CAB = 180 [Angle Addition Postulate.]
Step 2: m∠CAD + 32° = 180° [Substitute.]
Step 3: m∠CAD = 148 [Simplify.]
Quick Summary
- Linear pairs are adjacent angles.
- Linear pairs form a straight line (180 degrees).
- The sum of the measures of angles in a linear pair is 180°.
🍎 Teacher Insights
Use visual aids and real-world examples (e.g., a straight road divided by an intersection) to illustrate the concept of linear pairs. Emphasize the importance of both adjacency and supplementary properties.🎓 Prerequisites
- Angles
- Adjacent Angles
- Supplementary Angles
Check Your Knowledge
Q1: If one angle in a linear pair measures 60°, what is the measure of the other angle?
Q2: Which of the following pairs of angles could be a linear pair?
Frequently Asked Questions
Q: Are all supplementary angles a linear pair?
A: No, supplementary angles only need to add up to 180 degrees. Linear pairs must also be adjacent.
Q: Can a linear pair consist of two right angles?
A: Yes, two 90-degree angles can form a linear pair since they are adjacent and add up to 180 degrees.