Pairs of Angles in Geometry

There are three main types of angles—acute, right, and obtuse. Acute angles measure less than 90 degrees, right angles measure exactly 90 degrees, and obtuse angles measure more than 90 degrees but less than 180 degrees. However, there are also two types of pairs of angles—complementary and supplementary. Complementary angles add up to 90 degrees while supplementary angles add up to 180 degrees. Here’s a more in-depth look at each type of pair of angles.

Complementary Angles

As we just mentioned, complementary angles always add up to 90 degrees. This means that if you know one angle in a pair, you can always find the other angle by subtracting the known angle from 90 degrees. For example, if Angle A measures 30 degrees, then Angle B must measure 60 degrees because 30 + 60 = 90.

There are two special cases when it comes to complementary angles. The first is when one of the angles is a right angle. In this case, the other angle must be acute because the sum of an acute angle and a right angle is always 90 degrees. So, if Angle A is a right angle, then Angle B must measure less than 90 degrees. 

The second special case occurs when both angles are acute. In this case, the two angles are said to be complementary adjacent angles because they share a common vertex and side. Complementary adjacent angles are always adjacent (meaning they share a common vertex) and their non-shared sides form a line. In other words, they form a straight line! 

Supplementary Angles

Supplementary angles always add up to 180 degrees—but what happens when one or both of the angles is obtuse? That’s where things get a bit tricky. Remember that an obtuse angle measures more than 90 degrees but less than 180 degrees. This means that if Angle A is obtuse and we know that Angle B is supplementary to Angle A, then Angle B must also be obtuse because the sum of two obtuse angles is always greater than 180 degrees but less than 360 degrees (a full rotation). However, if only one angle is obtuse, then the other angle must be acute because the sum of an acute angle and an obtuse angle is always 180 degrees. 

Conclusion: 

There are three main types of angles—acute, right, and obtuse—and two main types of pairs of angles—complementary and supplementary. Complementary angles always add up to 90 degrees while supplementary angles always add up to 180 degrees. However, things can get tricky when one or both of the angles in a pair is obtuse because the sum of two obtuse angles is always greater than 180 but less than 360 (a full rotation). The best way to remember all of this information is to practice identifying different types of pairs of angles in geometry problems. With enough practice, you'll be able to identify them without even thinking about it!

FAQ

What is an angle pair in geometry?

An angle pair is two angles that are related to each other in some way. There are three main types of angle pairs—complementary, supplementary, and adjacent. Complementary angles add up to 90 degrees while supplementary angles add up to 180 degrees. Adjacent angles share a common vertex and side but do not necessarily have any mathematical relationship.

What are the 4 types of angle pairs?

There are four types of angle pairs—complementary, supplementary, adjacent, and vertical. Complementary angles add up to 90 degrees while supplementary angles add up to 180 degrees. Adjacent angles share a common vertex and side but do not necessarily have any mathematical relationship. Vertical angles are angles that are opposite each other and share the same vertex.

How many pairs of angles are there in geometry?

There are three main types of angle pairs—complementary, supplementary, and adjacent. Complementary angles add up to 90 degrees while supplementary angles add up to 180 degrees. Adjacent angles share a common vertex and side but do not necessarily have any mathematical relationship.

What are the 5 pairs of angles?

There are five pairs of angles—acute, right, obtuse, complementary, and supplementary. Acute angles measure less than 90 degrees while right angles measure exactly 90 degrees. Obtuse angles measure greater than 90 degrees but less than 180 degrees. Complementary angles add up to 90 degrees while supplementary angles add up to 180 degrees.