Profile
Settings
Refer your friends
Sign out
In geometry, a linear pair of angles is a pair of adjacent angles formed when two lines intersect each other at a point. Adjacent angles are formed when two angles have a common vertex and a common arm but do not overlap each other. The linear pair of angles is always supplementary as it forms on a straight line. In other words, the sum of the two angles in a linear pair is always 180°
Linear Pair of Angles Definition:
When two lines intersect each other at a single point, linear pairs of angles are formed at that point. If the angles formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose sum of measures is 180°.
Properties of Linear Pair of Angles:
There are some properties of linear pairs of angles that make it unique and different from other types of angles. The properties of linear pair of angles are listed below:
- The sum of two angles in any linear pair is always 180°.
- All the linear pairs of angles are adjacent angles but all adjacent angles are not linear pairs.
- The Linear pair of angles share the common vertex and a common arm between them.
- They always form a straight line that is 180° angle.
- They can be considered as two parts of a 180-degree angle.
Linear Pair of Angles Vs Supplementary Angles:
In geometry, there are two types of angles whose sum results in 180 degrees, They are linear pairs of angles and supplementary angles. We generally say that the linear pair of angles are supplementary, but do you know that these two types of angles are not the same? Let us understand the difference between supplementary angles and linear pair of angles by the table given below:
Linear Pair of Angles | Supplementary Angles |
|---|---|
These angles are always adjacent. It means, a pair of angles whose sum is 180 degrees and they lie next to each other sharing a common vertex and a common arm/line is known as a linear pair of angles. | These angles need not be adjacent. But the sum of those angles is 180°. |
All the linear pairs are supplementary angles. | Supplementary angles are not linear pairs. |
Example: ∠1 and ∠2 in the image given in the diagram below. | Example: ∠A and ∠B, ∠1 and ∠2 (in the image given below). |
Linear Pair Postulate:
The linear pair postulate states that if a ray stands on a line, then the sum of two adjacent angles will be 180o. Is the converse of this statement true? That is, if the sum of a pair of adjacent angles is 180o, will the non-common arms of those two angles form a line?…… Yes, the converse is true. These two axioms are grouped together as linear pair axioms. In the figure, ray QS stands on a line PR forming a linear pair of angles ∠1 and ∠2.
Important Notes:
- In a linear pair, if the two angles have a common vertex and a common arm/line, then the non-common side makes a straight line and the sum of the measure of angles is always 180°.
- The Linear pairs are always supplementary.
- The Linear pairs of angles are not congruent every time.
conclusion :
Linear pairs of angles are formed when two lines intersect/meet each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the lines. The sum of angles of a linear pair is equal to 180°. Such types of angles are also known as supplementary angles. The adjacent angles are those that have a common vertex. so, here as well the linear angles have a common vertex. Also, there will be a common angle arm/line that represents both the angles. A real-life example of a linear pair is a ladder that is placed against a wall, forming linear angles at the ground.
Linearity represents one that is straight. So here also, linear angles are the ones that are formed into straight lines. The pair of adjacent angles here are constructed to a line segment, but not all adjacent angles are linear. Hence, we can also say that linear pairs of angles are the adjacent angles whose non-common arms are actually opposite rays.
