# Complementary and Supplementary Angles

#### Grade 7 Math Worksheets

**Complementary angles are two angles that add up to 90 degrees. Supplementary angles, on the other hand, are two angles that add up to 180 degrees.**

Table of Contents:

- Complementary and Supplementary Angles
- Formulas for Supplementary Angles
- Formulas for Complementary Angles
- Solved Examples
- FAQs

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## Complementary and Supplementary Angles - Grade 7 Math Worksheet PDF

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## Complementary and Supplementary Angles

Complementary and supplementary angles are two types of angles that are commonly used in geometry.

Complementary angles are two angles that add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees. Complementary angles are often denoted as “C.A.” or “∠C” for short. Examples of complementary angles include 30 degrees and 60 degrees, or 45 degrees and 45 degrees.

Supplementary angles, on the other hand, are two angles that add up to 180 degrees. If angle C and angle D are supplementary, then C + D = 180 degrees. Supplementary angles are often denoted as “S.A.” or “∠S” for short. Examples of supplementary angles include 120 degrees and 60 degrees, or 135 degrees and 45 degrees.

It is important to note that complementary and supplementary angles do not have to be adjacent angles (angles that share a common vertex and side). They can be any two angles that add up to 90 degrees or 180 degrees, respectively.

Complementary and supplementary angles are used in a variety of geometric and trigonometric applications, including calculating the angles of right triangles and solving trigonometric equations.

## Formulas for Supplementary Angles

Supplementary angles are two angles that add up to 180 degrees. There are several formulas that can be used to find the measures of supplementary angles:

If the measures of two angles are known to be supplementary, and one angle is x degrees, then the measure of the other angle can be found by subtracting x from 180 degrees. This can be expressed as:

Measure of one angle + Measure of other angle = 180 degrees

x + Measure of other angle = 180 degrees

Measure of other angle = 180 – x degrees

If two angles are known to be supplementary, their measures can be found by solving a system of two equations. For example, if the two angles are x degrees and y degrees, and their sum is 180 degrees, the system of equations would be:

x + y = 180

solve for x or y using the first equation, for example x = 180 – y

substitute into the second equation:

x + y = 180

(180 – y) + y = 180

180 = 180

Therefore, x = 180 – y and y = 180 – x, and the measures of the two supplementary angles can be found by substituting in values for x or y.

## Formulas for Complementary Angles

Complementary angles are two angles that add up to 90 degrees. There are several formulas that can be used to find the measures of complementary angles:

If one angle is known, the other angle can be found by subtracting the known angle from 90 degrees. For example, if one angle is 35 degrees, the measure of the other angle is 90 – 35 = 55 degrees.

If the measures of two angles are known to be complementary, and one angle is x degrees, then the measure of the other angle can be found by subtracting x from 90 degrees. This can be expressed as:

Measure of one angle + Measure of other angle = 90 degrees

x + Measure of other angle = 90 degrees

Measure of other angle = 90 – x degrees

If two angles are known to be complementary, their measures can be found by solving a system of two equations. For example, if the two angles are x degrees and y degrees, and their sum is 90 degrees, the system of equations would be:

x + y = 90

solve for x or y using the first equation, for example x = 90 – y

substitute into the second equation:

x + y = 90

(90 – y) + y = 90

90 = 90

Therefore, x = 90 – y and y = 90 – x, and the measures of the two complementary angles can be found by substituting in values for x or y.

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## Solved Examples

**Example 1:** Find the measure of the complementary angle to an angle with a measure of 25 degrees.

**Solution:**

The measure of the complementary angle can be found by subtracting 25 from 90 degrees:

90 – 25 = 65 degrees.

Therefore, the measure of the complementary angle is 65 degrees.

**Example 2:** Two angles are supplementary, and one angle has a measure of 110 degrees. Find the measure of the other angle.

**Solution:**

The measure of the other angle can be found by subtracting 110 from 180 degrees:

180 – 110 = 70 degrees.

Therefore, the measure of the other angle is 70 degrees.

**Example 3:** Two angles are complementary, and one angle has a measure of 35 degrees. Find the measure of the other angle.

**Solution:**

The measure of the other angle can be found by subtracting 35 from 90 degrees:

90 – 35 = 55 degrees.

Therefore, the measure of the other angle is 55 degrees.

**Example 4:** Two angles are complementary, and their measures are in the ratio of 2:3. Find the measures of the angles.

**Solution:**

Let the measures of the angles be 2x and 3x, respectively.

Since the angles are complementary, we have the equation 2x + 3x = 90.

Simplifying this equation gives 5x = 90, so x = 18.

Therefore, the measures of the angles are:

2x = 2(18) = 36 degrees

3x = 3(18) = 54 degrees.

The first angle measures 36 degrees, and the second angle measures 54 degrees.

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## Complementary and Supplementary Angles FAQS

##### What is the difference between complementary angles and supplementary angles?

Complementary angles are two angles that add up to 90 degrees, while supplementary angles are two angles that add up to 180 degrees.

##### What is the formula for finding the measure of a complementary angle?

If one angle is known, the measure of the complementary angle can be found by subtracting the known angle from 90 degrees.

##### What is the formula for finding the measure of a supplementary angle?

If one angle is known, the measure of the supplementary angle can be found by subtracting the known angle from 180 degrees.

##### How do I solve a problem involving complementary or supplementary angles?

First, identify the relationship between the two angles (complementary or supplementary), and then use the appropriate formula to find the measure of the missing angle. Make sure to check your work by verifying that the sum of the two angles equals 90 degrees (for complementary angles) or 180 degrees (for supplementary angles).

##### Can two angles be both complementary and supplementary?

No, two angles cannot be both complementary and supplementary at the same time, since the sum of complementary angles is 90 degrees and the sum of supplementary angles is 180 degrees.

**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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