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Lesson 2Adjacent Angles

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.

2.1 Estimating Angle Measures

Estimate the degree measure of each indicated angle.

8 sets of angles are shown

2.2 Cutting Rectangles

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 rectangle is shown
  1. 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.)
  2. On each of these two pieces, measure the angle that is marked by part of a circle. Label the angle measure on the piece.
  3. What do you notice about these angle measures?
  4. Clare measured 70 degrees on one of her pieces. Predict the angle measure of her other piece.
  1. On the other rectangular paper, draw a small quarter-circle in one of the corners.
  2. Repeat the previous steps to cut, measure, and label the two angles marked by part of a circle.
A rectangle is shown
  1. What do you notice about these angle measures?
  2. Priya measured 53 degrees on one of her pieces. Predict the angle measure of her other piece.

2.3 Is It a Complement or Supplement?

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

    1. BCA
    2. BCD
    A protractor is measuring angles in a rectangle.

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

  2. Use the protractor in the picture to find the measure of angles:

    1. LOK
    2. LOM
    A protractor is measuring angles in a rectangle.

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

  1. Angle BAC is a right angle. Find the measure of angle CAD .
Angle BAD is 64 degrees. Angle BAD and CAD form a straight angle.
  1. Point O is on line RS . Find the measure of angle SOP .
Angle ROP is 76 degrees. Angle SOP and Angle ROP form a straight angle.

Are you ready for more?

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 piece of paper has a fold in it.
A piece of paper with 2 folds in it.
A piece of paper has a few folds in it.
  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 2 Summary

If two angle measures add up to 90^\circ , then we say the angles are complementary. Here are three examples of pairs of complementary angles.

Three sets of angles.

If two angle measures add up to 180^\circ , then we say the angles are supplementary. Here are three examples of pairs of supplementary angles.

4 sets of angles

Glossary Terms

complementary

Complementary angles have measures that add up to 90 degrees.

For example, a 15^\circ angle and a 75^\circ angle are complementary. 

An image of two angles are shown. One angle is 75 degree and the other is 15 degrees. These are complementary.
An image of two angles are shown. One angle is 75 degree and the other is 15 degrees. These are complementary.
supplementary

Supplementary angles have measures that add up to 180 degrees.

For example, a 15^\circ  angle and a 165^\circ angle are supplementary.

Two angles are shown. One is 165 degrees and the other is 15 degrees.
Two angles are shown. One is 165 degrees and the other is 15 degrees.

Lesson 2 Practice Problems

  1. Angles A and C are supplementary. Find the measure of angle C .

    Angle EAB is 74 degrees. Angle FCD is undetermined.

    1. List two pairs of angles in square CDFG that are complementary.

    1. Name three angles that sum to 180^\circ .
    A square is made up of three triangles. Traingle CDM has angles of 27, 90, and 63 degrees. Traingle GFM has angles of 26, 90, and 64 degrees.

  3. Complete the equation with a number that makes the expression on the right side of the equal sign equivalent to the expression on the left side.

    5x-2.5 +6x-3 = \underline{\ \ \ \ }(2x-1)

  4. Match each table with the equation that represents the same proportional relationship.

    1. x y
      2 8
      3 12
      4 16
      5 20
    2. x y
      3 4.5
      6 9
      7 10.5
      10 15
    3. x y
      2 \frac52
      4 5
      6 \frac{15}{2}
      12 15
    1. y=1.5x
    2. y=1.25x
    3. y=4x