The purpose of this activity is to provide a tangible experience with complementary and supplementary angles, which will be formally defined in a later activity. Students cut sheets of paper in two ways to see the decomposition of straight and right angles. In later activities and lessons, students will continue working with the fact that specific angles can be composed to make straight or right angles as they make sense of the relationship between these pairs of angles (MP1). They use informal language to describe the relationships between angles in this activity.

For the whole-group discussion, select students who came up with a variety of angle measures, and ask them to share their angles pairs.

Invite previously selected students to display pairs of angles that make up the side of a rectangle. Ask, “What did your groups notice about the angle pairs that made up the side of the rectangle? What do these angle pairs have in common?” (Each angle measure could be different, but the pair added up to 180 degrees. They make the side of a rectangle, which is a straight line.)

Invite previously selected students to display pairs of angles that make up the corner of a rectangle. Ask, “What did your groups notice about the angle pairs that made up the corner of the rectangle? What do these angle pairs have in common?” (Each angle measure could be different, but the pair added up to 90 degrees. They make the corner of a rectangle, which is a right angle.)

Ask students to think about how they solved for the measure of Clare’s second angle compared to how they solved for the measure of Priya’s second angle. “What was the same, and what was different?” (Since Clare’s angles made up the side of the rectangle, they had to add up to 180 degrees, but Priya’s had to add up to 90 degrees.) 
 

In this activity, students the generalize process for finding the measures of angles that are complements and supplements of angles with known measures, based on repeated observations of the relationships of these angles (MP8). After they have worked on the activity and shared their solutions, they are introduced to the vocabulary terms complementary and supplementary.

Monitor for students who use or explain different ways to calculate the unknown angle measure. For example, when finding the measure of angle , some might write and some might write .

The goal of this discussion is to introduce students to the terms complementary and supplementary for describing relationships between pairs of angles.

First, have students compare answers and strategies, with their partners, for the last two questions.

Next, display these images from the activity, and ask students which images are similar and in what way. (Figures 1 and 2 both show a protractor, and Figures 3 and 4 don’t. Figures 1 and 3 show angles that add up to 90 degrees, and Figures 2 and 4 show angles that add up to 180 degrees.

Figure 1

A protractor is shown.  Point C is on the center of the protractor. Segment B, A lies along the 0 or 180 line, segment C D lies along the 90 degree line. Segment A, C goes through the 30 or 130 line. Points A and B are connected, and points A and D are connected.

Figure 2

Figure 3

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Figure 4

Tell students that the term complementary describes a pair of angles whose measures have a sum of 90 degrees, and the term supplementary describes a pair of angles whose measures have a sum of 180 degrees. It is not important at this point to discuss that complementary or supplementary angles do not need to be adjacent, as that will be explored in the next lesson. Ask:

• “Which angles in this activity were supplementary angles?” (angles and , as well as angles and )
• “Which angles in this activity were complementary angles?” (angles  and , as well as angles and or angles and , or even  angles and )

Invite students to continue practicing using the words "complementary" and "supplementary" throughout the rest of this unit, so they can start to feel more comfortable using them in their vocabulary.