## Properties of Supplementary Angles

In geometry, two angles whose measures sum to 180 degrees are **supplementary angles**. These angles may share a common side, a common vertex, or have no points in common.

Let's look at some examples of supplementary angle pairs.

- 10 degrees and 170 degrees
- 30 degrees and 150 degrees
- 50 degrees and 130 degrees
- 70 degrees and 110 degrees
**90 degrees and 90 degrees**

Perhaps you noticed a pattern in this list - except for one pair of two right angles, all the supplementary angle pairs had one acute angle and one obtuse angle. This is an important property of supplementary angles - you will either have two right angles in the supplementary pair, or one acute angle and one obtuse angle.

Remember, only a pair of angles can be supplementary. Sure, the three angles in a triangle may add up to 180 degrees, but there are three angles in a triangle, so they are not supplementary!

## Theorems Involving Supplementary Angles

There are a number of theorems in geometry that involve supplementary angles. Keep in mind that since they are theorems, you could end up having to prove that they are true when you take a geometry class!

**Which pair of angles are always congruent?**

A linear pair forms a straight **angle** which contains 180º, so you have 2 **angles** whose measures add to 180, which means they are **supplementary**. If two **congruent angles** form a linear pair, the **angles are right angles**. If two **congruent angles** add to 180º, each **angle** contains 90º, forming **right angles**.

A **linear pair** forms a straight angle which contains 180º, so you have **2** angles whose measures add to 180, which means they are supplementary. If two congruent angles form a **linear pair**, the angles are right angles.

Given: ∠1 and ∠2 form a linear pair

Proof: ∠ 1 and ∠ 2 are supplementary

Statement Reason

∠1 and ∠2 form a linear pair given

Ray AB and Ray BC form a line definition of linear pair

m ∠ABC = 180° definition of straight line

m∠1+ m∠2 = ∠ABC ∠addition postulate

m∠1 + m∠2 = = 180° Substitution

∠1 and ∠2 are supplementary definition of supplementary ∠

Linear Pair Theorem: If 2 angles form a linear pair then they are supplementary

THE ANSWER IS YES

180/2 = 90

∠1 + ∠2 = <A-------B-------C>

90° + 90° = 180°

**Congruent Meaning**

**Congruent angles** are two or more **angles** that have the same measure. In simple words, they have the same number of degrees. It's important to note that the length of the **angles**' edges or the direction of the **angles** has no effect on their congruency. As long as their measure is equal, the **angles** are considered **congruent**

**Supplementary Meaning**

**Supplementary angles** are 2 **angles** that have the sum of 180 degrees. Therefore, the **requirement of supplementary angles** is to have the 2 **angles** to equal 180 degrees.

Thanks Again

Your Tutor

Mr. Julio Lopez, Jr.