Linear pair
Linear Pair is a Grade 8 geometry concept in Saxon Math Course 3, Chapter 2, where students learn that two adjacent angles forming a straight line together measure exactly 180 degrees and are therefore supplementary. Recognizing linear pairs allows students to set up and solve equations to find unknown angle measures in geometric figures.
Key Concepts
Property If two angles together form a straight angle, they are called a linear pair . The sum of their measures is always $180^\circ$.
Examples If $\angle A$ and $\angle B$ form a linear pair and $m\angle A = 80^\circ$, then $m\angle B = 180^\circ 80^\circ = 100^\circ$. When a door is partially open, the angle of the door and the angle of the remaining space to the wall form a linear pair. In the lesson's diagram, if $m\angle DMC = 45^\circ$, then $m\angle CMA = 180^\circ 45^\circ = 135^\circ$ as they are a linear pair.
Explanation Think of a linear pair as two friendly angles sitting side by side on a straight line. They share a vertex and a side, and their other sides form a perfect straight path. Because a straight line is $180^\circ$, these two angle buddies will always add up to $180^\circ$, no matter what their individual sizes are.
Common Questions
What is a linear pair in geometry?
A linear pair consists of two adjacent angles whose non-common sides form a straight line. The two angles in a linear pair are supplementary and always add up to 180 degrees.
How is a linear pair different from supplementary angles?
All linear pairs are supplementary, but not all supplementary angles form a linear pair. Linear pairs must also be adjacent and share a common side.
How do you find a missing angle in a linear pair?
Subtract the known angle from 180 degrees. For example, if one angle is 65 degrees, the other is 180 minus 65 = 115 degrees.
What does it mean for angles to be adjacent?
Adjacent angles share a common vertex and a common side but do not overlap.
Where is the linear pair concept taught in Grade 8?
Linear pairs are covered in Saxon Math Course 3, Chapter 2: Number and Operations and Geometry.