Supplementary angles are two angles whose sum is 180 degree. A linear pair (two angles that form a line) will always be supplementary. The two angles can be adjacent or non-adjacent.

Linear Pair of Angles:
A linear pair of angles is formed when two angles are adjacent (share a common vertex and side) and their non-common sides are opposite rays. In other words, the two angles are formed by two intersecting lines and their sum is always equal to 180 degrees.

Definition:
Two angles forming a linear pair are always supplementary, which means their sum is always equal to 180 degrees.

Explanation:
When two lines intersect, they form four angles. The angles that are opposite to each other and share a common vertex are called vertically opposite angles and are always equal. The other two angles that are adjacent to each other and share a common vertex are called adjacent angles. When these adjacent angles form a straight line (180 degrees), they are known as a linear pair of angles.

To understand this concept better, let's consider an example:

Example:
Consider two lines AB and CD intersecting each other at point O. Let the angles formed be ∠AOC and ∠BOD. These two angles are adjacent to each other and share a common vertex O. Since the lines AB and CD form a straight line, ∠AOC and ∠BOD are a linear pair of angles.

Properties of Linear Pair of Angles:
1. Linear pair of angles are always adjacent.
2. Linear pair of angles are always supplementary.
- Supplementary angles are two angles whose sum is 180 degrees.
- In a linear pair, the sum of the two angles is always 180 degrees.

Conclusion:
In conclusion, two angles forming a linear pair are always supplementary, which means their sum is always equal to 180 degrees. This property holds true for any pair of adjacent angles that form a straight line.

90degree is the length of both the linear pair that y it is supplementary.......