Let’s look at some special pairs of angles.

2.1: Estimating Angle Measures

Estimate the degree measure of each indicated angle.

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.

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.

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. $BCD$

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. $LOM$

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 $CAD$.

1. Point $O$ is on line $RS$. Find the measure of angle $SOP$.

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.

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.

Glossary

complementary

complementary

Two angles are complementary to each other if their measures add up to $90^\circ$. The two acute angles in a right triangle are complementary to each other.

supplementary

supplementary

Two angles are supplementary to each other if their measures add up to $180^\circ$.

For example, angle $ABC$ is supplementary to angle $CBD$, because they add up to a straight angle, which has measure $180^\circ$.