Lesson 2Adjacent Angles

Learning Goal

Let’s look at some special pairs of angles.

Learning Targets

  • I can find unknown angle measures by reasoning about complementary or supplementary angles.

  • I can recognize when adjacent angles are complementary or supplementary.

Lesson Terms

  • adjacent angles
  • complementary
  • right angle
  • straight angle
  • supplementary

Warm Up: Estimating Angle Measures

Problem 1

Estimate the degree measure of each indicated angle.

8 diagrams of two intersecting lines forming angles

Activity 1: Cutting Rectangles

Problem 1

Your teacher will give you two small, rectangular papers.

  1. On one of the papers, draw a small half-circle in the middle of one side.

    A paper with a half circle drawn in the middle on one side.

  2. Cut a straight line, starting from the center of the half-circle, all the way across the paper to make 2 separate pieces. (Your cut does not need to be perpendicular to the side of the paper.)

  3. On each of these two pieces, measure the angle that is marked by part of a circle. Label the angle measure on the piece.

  4. What do you notice about these angle measures?

  5. Clare measured 70 degrees on one of her pieces. Predict the angle measure of her other piece.

  6. On the other rectangular paper, draw a small quarter-circle in one of the corners.

    A piece of paper with a small quarter circle drawn in the lower right corner.

  7. Repeat the previous steps to cut, measure, and label the two angles marked by part of a circle.

  8. What do you notice about these angle measures?

  9. Priya measured 53 degrees on one of her pieces. Predict the angle measure of her other piece.

Activity 2: Is It a Complement or Supplement?

Problem 1

  1. Use the protractor in the picture to find the measure of angles and .

    A rectangle labeled ABCD with a diagonal from A to C. Point C is located in the bottom middle of a protractor.

  2. Explain how to find the measure of angle without repositioning the protractor.

  3. Use the protractor in the picture to find the measure of angles and .

    A rectangle labeled KLMN with a diagonal from K to center of protractor point O.

  4. Explain how to find the measure of angle without repositioning a protractor.

  5. Angle is a right angle. Find the measure of angle .

    Three lines intersecting at point A and end points B, C, D. Angle DAB is 64 angles.

  6. Point is on line . Find the measure of angle .

    Two lines that intersect at point O making a 76 degree angle.

Are you ready for more?

Problem 1

Clare started with a rectangular piece of paper. She folded up one corner, and then folded up the other corner, as shown in the photos.

A photo of a piece of paper with flowers on it.
A hand folding the paper.
The piece of paper showing the fold lines.

  1. Try this yourself with any rectangular paper. Fold the left corner up at any angle, and then fold the right corner up so that the edges of the paper meet.

  2. Clare thought that the angle at the bottom looked like a 90 degree angle. Does yours also look like it is 90 degrees?

  3. Can you explain why the bottom angle always has to be 90 degrees? Hint: the third photo shows Clare’s paper, unfolded. The crease marks have dashed lines, and the line where the two paper edges met have a solid line. Mark these on your own paper as well.

Lesson Summary

If two angle measures add up to , then we say the angles are complementary. Here are three examples of pairs of complementary angles.

Three examples of pairs of complementary angles. First are 30 and 60 degree angles, next two 45 degree angles, and a triangle with 2 angles - 38 and 52.

If two angle measures add up to , then we say the angles are supplementary. Here are three examples of pairs of supplementary angles.

Three examples of pairs of supplementary angles. First are 55 and 125 degrees, next two 90 degree angles, and two separate diagrams with 152 and 28 degree angles