Supplementary angles might sound like a big, fancy term, but don’t worry—they’re actually simple and fun to learn about!
We created this beginner-friendly guide to help you master supplementary angles.
We’ll start with a simple definition and explain how to recognize them. Then, we’ll dive into the different types of supplementary angles, work through some solved examples together, and wrap up with a quick quiz to test your knowledge. Let’s dive into it!
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Supplementary angles are two angles that add up to 180° (degrees).
Regardless of their position, as long as the sum of two angles equals 180°, they are considered supplementary angles. This relationship remains true whether the angles are positioned next to each other or are entirely separate.
To better understand supplementary angles, let's explore their key characteristics and the terminology used to describe them:
Always Total 180°: No matter how they are placed, two angles must always add up to 180° to be considered supplementary.
Supplementary Relationship: Each angle in the pair is the supplement of the other. For example, if one angle is 110°, the other must be 70° because 110° + 70° = 180°.
Straight Angle Connection: A straight angle measures exactly 180°, meaning that when two supplementary angles are adjacent, they form a linear pair and create a straight line.
Acute and Obtuse Pairing: In most cases, one angle in a supplementary pair is acute (less than 90°) and the other is obtuse (greater than 90° but less than 180°). The only exception is when both angles are right angles (90° each), which also sum to 180°.
By recognizing these properties, you can easily identify and work with supplementary angles, whether in geometry problems, real-world applications, or standardized tests!
Supplementary angles have a 'smaller' sibling called "complementary angles." It's easy to tell the two apart!
Complementary angles add up to 90°, forming the “right angle” which looks like the corner of a square. A quick way to remember it is by the letter "C" for Corner.
On the other hand, supplementary angles add up to 180°, just like a straight line. Remember "S" for Straight lines.
Let’s keep exploring the supplementary angles!
Supplementary angles can appear in different forms, depending on how they are positioned relative to each other.
While all supplementary angles add up to 180°, their arrangement affects how they interact in geometric problems and real-world applications.
Some supplementary angles share a common side and form a straight line, while others exist separately but still maintain their sum of 180°.
Understanding these types will help you identify supplementary angles in various scenarios, from solving equations to recognizing patterns in everyday life.
Let’s explore the two main types of supplementary angles: adjacent and non-adjacent.
Adjacent supplementary angles are a supplementary angle pair that shares a vertex (the point where the lines meet) and a common side (the line that connects the vertex of both angles).
Think of it like this:
Imagine two angles sitting right next to each other, sharing one of their sides. If these two angles together form a straight line (180°), they are considered adjacent supplementary angles.
Unlike adjacent supplementary angles, non-adjacent supplementary angles do not share a common vertex or side. They can be located anywhere in space—on different lines, within different shapes, or even on separate diagrams.
The only requirement is that their sum must equal 180°.
Let’s look at an example!
Imagine you have two triangles. One triangle has an angle measuring 100°. In a completely different triangle, there's an angle measuring 80°.
Even though these angles are not connected, they are still supplementary because 100° + 80° = 180°.
Now that we know that supplementary angles are two angles which add up to 180°, calculating the unknown supplementary angle is easy!
If one angle measures 75°, what is its supplementary angle?
Let's go back to the basics:
We know that supplementary angles are two angles that equal 180° together.
So, to find our missing angle, let's work backwards!
All we have to do is subtract the angle we know from the total which is 180°.
180° - 75° = 105°
So, the supplementary angle of 75° is 105°.
Two adjacent supplementary angles are in a ratio of 2:3. What are their measures?
Let’s write that mathematically: one angle is 2x, the other is 3x, and together they equal 180°.
2x + 3x = 180°
5x = 180°
x = 180° ÷ 5
x = 36°
We found the x, so now we can calculate our angles:
2x = 2 × 36° = 72°
3x = 3 × 36° = 108°
There we have it! Our two angles measure 72° and 108°.
Now it's your turn to put your knowledge to the test!
Solve the problems below and check your answers at the end to see how well you understand supplementary angles. You've got this!
If one angle is 130°, what is its supplementary angle?
Two angles are supplementary. If one is three times the other, find the angles.
Two adjacent angles form a straight line. If one is 85°, what is the other?
A triangle has one angle measuring 40°. Can you find an angle outside the triangle that makes a supplementary pair with it?
No. Supplementary angles must be two angles that add up to 180°.
No. An obtuse angle is greater than 90°, and two obtuse angles will always add to more than 180°.
Yes! A linear pair is a pair of adjacent angles that form a straight line, which always means they are supplementary.
Yes! Since a right angle measures 90°, two right angles add up to 180°, making them supplementary.
No. An acute angle is less than 90°. If you add two acute angles together, their sum will always be less than 180°, so they cannot be supplementary.
No. Vertical angles are equal in measure but are not necessarily supplementary. For example, if two vertical angles each measure 45°, their sum is 90°, not 180°.
No. They can be separate and unrelated angles as long as their measures add up to 180°. For example, one angle could be in a triangle, and another could be in a different shape.
No. A reflex angle is greater than 180°, so there is no second angle that can make their sum exactly 180°.
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180° - 130° = 50°
Let the angles be x and 3x:
180° - 85° = 95°
The angle outside the triangle would be 140° (since 40° + 140° = 180°).
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