We already know what angles are, Let us now focus on Linear pair of angles.

When the angle between two lines is 180Â°, they form a straight angle. A straight angle is just another way to represent a straight line. A straight line can be visualized as a circle with infinite radius. Line segment is any portion of a line which has two end points. Also, a portion of any line with only one end point is called a ray. A line segment with \(A\)

If a point *O* is taken anywhere on the line segment \(\overline{AB}\)*AO* and *OB* is a straight angle i.e. 180Â°.

Consider a ray \(\overrightarrow{OP}\)

The angles which are formed at *O* are âˆ *POB* and âˆ *POA*. It is known that the angle between the two line segments AO and OB is 180Â°. therefore, the angles âˆ *POB* and âˆ *POA* add up to 180Â°.

Thus, âˆ *POB* + âˆ *POA* = âˆ *AOB* = \(180Â°\)

âˆ POB and âˆ POA are adjacent to each other and when the sum of adjacent angles is 180Â° then such angles form linear pair of angles.

The above discussion can be stated as an axiom:

Axiom 1: If a ray stands on a line then the adjacent angles form a linear pair of angles.

In the figure 2 given above, all the line segments pass through the point O as shown. As the ray \(\overrightarrow{OA}\)*AOD* and âˆ *AOC* form a linear pair. Similarly, âˆ *QOD* and âˆ *POD* form a linear pair and so on.

The converse of the stated axiom is also true, which can also be stated as the following axiom:

Axiom 2: If two angles form a linear pair, then uncommon arms of both the angles form a straight line.

Figure 3 Adjacent angles with different measures

In the figure shown above, only the last one represents a linear pair, as the sum of the adjacent angles is 180Â°. Therefore, *AB* represents a line. The other two pairs of angles are adjacent but they do not form a linear pair. They do not form a straight line.

The two axioms mentioned above form the Linear Pair Axioms and are very helpful in solving various mathematical problems. There is a lot more to learn about lines and angles. To know more about properties of pair of angles, download BYJUâ€™s-The Learning App from Google Play Store.