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Two angles are said to be supplementary angles if they add up to 180 degrees. Supplementary angles form a straight angle (180 degrees) when they are put together. In other words, angle 1 and angle 2 are supplementary, if Angle 1 + Angle 2 = 180^{°}. In this case, Angle 1 and Angle 2 are called "supplements" of each other. Two angles x° and y° are said to be supplementary if. x° + y° = 180° The supplement of an angle x° is obtained by subtracting it from 180°. Supplement of x° = (180 - x)°. If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary angles. Theorem 10.5: If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary angles. As we know, if the sum of two angles is equal to 180°, then they are supplementary angles. Each of the angles is said to be a supplement of another angle. Hence, we can determine the supplement of an angle, by subtracting it from 180°.

For example, if you had given that two angles that form supplementary angles. If one angle is ∠A then another angle ∠B is its supplement. Hence,

**∠****A = 180° – ****∠****B (or)**

**∠****B = 180° – ****∠****A**

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees. The two supplementary angles, if joined together, form a straight line and a straight angle. But it should be noted that the two angles that are supplementary to each other, do not have to be next to each other. Hence, any two angles can be supplementary angles, if their sum is equal to 180°. Geometry is one of the important branches of mathematics that deals with the study of different shapes. It initiates the study of lines and angles. A straight line is a line without curves and it is defined as the shortest distance between two points. An angle is formed when the line segment meets at a point. Some of the examples of supplementary angles are: 120° + 60° = 180°, 90° + 90° = 180°, 140° + 40° = 180°, 96° + 84° = 180°

**The important properties of supplementary angles are:**

- The two angles are said to be supplementary angles when they add up to 180°.
- The two angles together make a straight line, but the angles need not be together.
- “
” of supplementary angles stands for the “**S****S**traight” line. This means they form 180°.

There are two types of Supplementary angles: adjacent and non-adjacent angles

**A: Adjacent Supplementary Angles:**

The supplementary angles that have a common arm and a common vertex are called adjacent supplementary angles. The adjacent supplementary angles share the common line segment and vertex with each other.

For example, the supplementary angles 110° and 70°, in the given figure, are adjacent to each other. The adjacent angles will have the common side and the common vertex. Two angles are said to be supplementary angles if the sum of both the angles is 180 degrees. If the two supplementary angles are adjacent to each other then they are called linear pair.

**B: Non-adjacent Supplementary Angles :**

The supplementary angles that do not have a common arm and a common vertex are called non-adjacent supplementary angles. The non-adjacent supplementary angles do not share the line segment or vertex with each other. For example, the supplementary angles 130° and 50°, in the given figure, are non-adjacent to each other.

In the figure, ∠1 and ∠3 are non-adjacent angles. They share a common vertex, but not a common side. Angles ∠1 and ∠2 are non-adjacent angles. Vertical angles are two nonadjacent angles formed by two intersecting lines

The supplementary angle theorem states that if two angles are supplementary to the same angle, then the two angles are said to be congruent.

**Proof:**

If ∠x and ∠y are two different angles that are supplementary to a third angle ∠z, such that,

∠x + ∠z = 180 ……. (1)

∠y + ∠z = 180 ……. (2)

Then, from the above two equations, we can say,

∠x = ∠y

Hence proved..

Finding the measure of an unknown angle from the given figure.

We know that the supplementary angles add up to 180**°.**

X + 55° + 40° = 180°

X + 95° = 180°

X = 180°- 95°

X = 85°

Therefore, the unknown angle, X = 85°

The two given angles are supplementary. If the estimate of the angle is two times the estimate of the other, what is the measure of each angle?

**Answer: **

Assume the measure of one of the angles that are supplementary to be “a”.

The estimate of the angle is two times the estimate of the other.

The measure of the other angle is 2a.

If the total of the estimates of the given two angles is 180°, then the angles are termed supplementary. Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees. The two supplementary angles, if joined together, form a straight line and a straight angle. But it should be noted that the two angles that are supplementary to each other, do not have to be next to each other. Hence, any two angles can be supplementary angles, if their sum is equal to 180°. Geometry is one of the important branches of mathematics that deals with the study of different shapes. It initiates the study of lines and angles. A straight line is a line without curves and it is defined as the shortest distance between two points. An angle is formed when the line segment meets at a point

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