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Supplementary Angles

Supplementary angles are two angles whose sum is 180 degrees. If you have two angles and you add their measures together, and the result is 180 degrees, then the angles are supplementary.

• Supplementary Angles
• Formula for Supplementary Angles
• Solved Examples
• FAQs

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Angles

Angles are geometric figures formed by two rays that share a common endpoint called the angle’s vertex. The two rays are usually denoted by a line segment with a dot in the middle representing the vertex.

The size of an angle is measured in degrees, which is a unit of angular measurement. A full circle has 360 degrees, and an angle can have any size less than or equal to 360 degrees.

Some common types of angles include:

• Acute Angle: an angle that measures less than 90 degrees
• Right Angle: an angle that measures exactly 90 degrees
• Obtuse Angle: an angle that measures more than 90 degrees but less than 180 degrees
• Straight Angle: an angle that measures exactly 180 degrees
• Reflex Angle: an angle that measures more than 180 degrees but less than 360 degrees

Angles can be added, subtracted, multiplied, and divided like numbers. Angles that add up to 90 degrees are called complementary angles, and angles that add up to 180 degrees are called supplementary angles.

Supplementary Angles

Supplementary angles are two angles whose sum is 180 degrees. In other words, if you have two angles and you add their measures together, and the result is 180 degrees, then the angles are supplementary.

For example, if one angle measures 120 degrees, then the other angle that is supplementary to it would measure 60 degrees. If one angle measures 70 degrees, then the other angle that is supplementary to it would measure 110 degrees.

Supplementary angles can be formed in many different ways, such as by two intersecting lines, or by a line intersecting a pair of parallel lines. When two lines intersect, the opposite angles are always supplementary.

For example, if you have two intersecting lines, and one angle measures 60 degrees, then the opposite angle must measure 120 degrees, since 60 + 120 = 180.

Supplementary angles are important in many areas of mathematics, including geometry and trigonometry. They can also be used in real-world applications, such as in engineering and construction, where angles need to be measured and adjusted to ensure proper alignment and stability.

Formula for Supplementary Angles

The formula for supplementary angles is quite simple. If two angles are supplementary, their measures add up to 180 degrees.

In mathematical notation, if we let angle A and angle B be two supplementary angles, we can write:

A + B = 180 degrees

This formula can be used to find the measure of one angle when the measure of the other angle is known. For example, if we know that angle A measures 70 degrees, we can find the measure of its supplementary angle B as follows:

A + B = 180 degrees

70 + B = 180

B = 180 – 70

B = 110

So the measure of angle B is 110 degrees, since it is supplementary to angle A which measures 70 degrees.

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Solved Examples for Supplementary Angles

Example 1: Find the measure of angle A if its supplementary angle B measures 120 degrees.

Solution: Since angle A and angle B are supplementary, we know that:

A + B = 180 degrees

We are given that B measures 120 degrees, so we can substitute that value into the equation:

A + 120 = 180

To solve for A, we can subtract 120 from both sides:

A = 180 – 120

A = 60

Therefore, the measure of angle A is 60 degrees.

Example 2: Two angles are supplementary. If one angle measures 30 degrees, what is the measure of the other angle?

Solution: We know that the two angles are supplementary, so their measures add up to 180 degrees. Let’s use the variable B to represent the measure of the other angle:

30 + B = 180

To solve for B, we can subtract 30 from both sides:

B = 180 – 30

B = 150

Therefore, the measure of the other angle is 150 degrees.

Example 3: Two angles are supplementary. If one angle measures x degrees, what is the measure of the other angle in terms of x?

Solution: We know that the two angles are supplementary, so their measures add up to 180 degrees. Let’s use the variable B to represent the measure of the other angle:

x + B = 180

To solve for B, we can subtract x from both sides:

B = 180 – x

Therefore, the measure of the other angle in terms of x is 180 – x degrees.

Supplementary Angles FAQS

What are supplementary angles?

Supplementary angles are two angles whose measures add up to 180 degrees.

How do you know if two angles are supplementary?

Two angles are supplementary if their measures add up to 180 degrees.

What is the formula for supplementary angles?

The formula for supplementary angles is A + B = 180 degrees, where A and B are the measures of the two angles.

Yes, supplementary angles can be adjacent, which means that they share a common vertex and one common side.

Can supplementary angles be complementary to each other?

No, supplementary angles cannot be complementary to each other, since complementary angles add up to 90 degrees, which is less than 180 degrees.

Are vertical angles supplementary?

Yes, vertical angles are always supplementary, since they are opposite angles formed by the intersection of two lines.

Can supplementary angles be obtuse?

Yes, one angle can be acute and the other obtuse, or both angles can be obtuse but they can’t be supplementary.

How can you use supplementary angles to solve problems?

You can use the formula A + B = 180 degrees to find the measure of one angle if the measure of the other angle is known, or to find the measures of both angles if the sum of their measures is known. Supplementary angles can be used in various real-world applications, such as in engineering and construction, where angles need to be measured and adjusted to ensure proper alignment and stability.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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