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
∠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 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 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.
Mr. Julio Lopez, Jr.