Linear pairs of angles are formed when two lines intersect 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 two lines. The sum of angles of a linear pair is always equal to 180°.
Such angles are also known as supplementary angles. The adjacent angles are the angles that have a common vertex. Hence, here as well the linear angles have a common vertex.
Also, there will be a common arm that represents both angles. A real-life example of a linear pair is a ladder which is placed against a wall and forms linear angles at the ground.
Linearity represents one which is straight. So here also, linear angles are the ones which are formed into a straight line.
The pair of adjacent angles here are constructed on a line segment, but not all adjacent angles are linear. Hence, we can also say, that a linear pair of angles is the adjacent angles whose non-common arms are opposite rays.
Explanation for Linear Pair of Angle
A straight angle is formed when the angle between two lines is 180 degrees. A straight line can be represented by using a straight angle. A circle of an infinite radius can be visualized on a straight line.
The line segment is any part of the line having two endpoints. Also, the ray is that part of the line which has only one endpoint. A line segment with A and B as two endpoints is represented as AB.
If there is a pair of adjacent angles, then the pair is called a linear angle only if their sum is equal to 180 degrees. For example, the linear pair of 40 degrees and 140 degrees will sum up to 180 degrees and thus, these adjacent angles will be known as linear angles.
The line segment AB and two arrows at the end indicate a line is represented in the figure given below.
If a point O is taken anywhere on the line segment AB as shown, then the angle between the two line segments AO and OB is straight i.e., 180°.
Real-Life Examples of Linear Pair
1. Ladder placed against the wall
A ladder placed against the wall is a real-life example of a Linear Pair. Here, the ‘angle A’ formed by placing the ladder against the wall is adjacent to ‘angle B.’ Both the angles formed have a common vertex and the sum equal to 180 degrees.
2. Hands of Clock
Here also, the angles A and B formed by the hands of the clock are adjacent to each other, have a common vertex, and the sum of both the angles is equal to 180 degrees.
3. Slices of Pizza
Generally, no one would think about stuff like mathematics while enjoying pizza with friends. But, if we see the intersections of pizza, we would notice the presence of Linear Pair angles. So, next time when you go to a pizza party don’t forget to salute the Linear Pair of angles.
4. Scissors
A pair of scissors is a classic example of a Linear Pair of angles, where the flanks of scissors, which are adjacent to each other and have common vertex O, form an angle of 180 degrees.
5. Electric Pole
An electric pole is also a real-life example of a Linear Pair. The angles P and Q qualify all the conditions to be considered as a Linear Pair.
6. Justice Balance
Another reason to be thankful to the Linear Pair of angles is that it is involved in delivering justice; as the angles formed in a justice-balance-machine are nothing but the Linear Pair of angles.
7. T-Junction
Whenever you go for a drive, don’t forget to notice the Linear Pair of angles formed at the T-junction.
8. Chopping Board
You would be surprised to know that the Linear Pair of angles is also formed on the chopping board. So, the next time you see your mother working in the kitchen and chopping vegetables to make delicious dishes for you, don’t forget to notice the Linear Pair of angles formed on the chopping board.