Lines, Angles, and Triangles: Lesson 3 - Complementary and Supplementary Angles

Complementary and Supplementary Angles is the third of eight self-paced lessons in the “Lines, Angles, and Triangles” section of KET’s GED^{®} Geometry Professional Development Online Course. This lesson focuses on the basics of complementary and supplementary angles and the importance of recognizing these angles in a context.

NOTE: This course was created based on the 2002 GED^{®} math test. The geometry instruction in this course is still valid, however, for up-to-date information about the 2014 GED^{®} math test, please visit KET’s GED^{®} Test Info: Mathematics online course.

On the GED^{®} Mathematics Test, students may need to apply their knowledge about angles to questions based on understanding specific angles as a sum of their measures.

Students will need to recognize complementary angles as two angles whose sum is 90˚.

Also, they will need to recall that a straight line is a straight angle, which is equal to 180˚. Supplementary angles are two angles whose sum is 180˚.

This lesson focuses on the basics of complementary and supplementary angles and on the importance of students recognizing them in a context. The challenge for many students is recognizing complementary and supplementary relationships in diagrams that have several labeled angles.

2Complementary Angles

Watch the video for an explanation of complementary and supplementary angles.

Angles: Complementary and Supplementary

Video: 1m 16s

Angles are measured in degrees. The symbol ° is used to show degrees.

A right angle is a square corner. A right angle measures 90°.

Question Juanita is making a quilt. She needs to cut two pieces of cloth and sew them together to form a square corner, as shown on the left. The design requires that both pieces have the same angle measure.

At what angle should she cut the pieces?

Step 1 Find the right angle where the two pieces of cloth are joined. Determine its measure.

A right angle measures 90°.

Step 2 Write an equation to find the measure of the two angles that form the right angle. Use x for each of the missing angles.

x + x = 90°

Step 3 Combine like terms. Then isolate x by performing the inverse operation to both sides of the equation.

Answer She should cut each piece at a 45° angle.

3Supplementary Angles

A straight angle looks like a straight line. A straight angle measures 180°.

Question Sofia must cut two pieces of tile so that their bases form a straight line.

If the first piece is cut at a 60° angle, at what angle must she cut the connecting piece?

Step 1 Determine the relationship between the 60° angle and the angle marked with a question mark (?).

The angles form a straight line, so they are supplementary. Their sum is 180°.

Step 2 Write an equation to find the measure of the two angles that form the right angle. Use x for each of the missing angles.

x + 60° = 180°

Step 3 Solve the equation. Isolate the x by subtracting 60 from both sides of the equation.

Answer She must cut a 120° angle.

4Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, consider how you would work through them with your students.

How could you help students to focus on the information they need and ignore the information they don’t need to solve the problems?

Lines, Angles, and Triangles: Complementary and Supplementary Angles Skill Review

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Printable Resource

In this lesson you have learned about complementary and supplementary angles. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.