The purpose of this activity is for students to practice solving equations that represent relationships between angles, in preparation for the next activity where students will write such equations themselves. In this activity, they compare the diagrams to possible equations in order to make sense of the structure of the equations and the angle relationships that they represent (MP7).

Select students to share equations they agreed with and angle measures they found for each problem. As students share their explanations, consider asking these questions:

• “Where do you see the relationship expressed in the equation in the given figure? (and vice versa)”
• “Did you and your partner agree on the equations and angle measures?”

For the last question, have students who used different equations to figure out the unknown angle measures share their explanations. Ask students:

• “What angle relationship did you need to recognize in order to use Elena’s equation?” (That the angle with a measure of w degrees and the angle measuring 148 degrees were supplementary.)
• “What angle relationship did you need to recognize in order to use Diego’s equation?” (That the angle measuring 148 degrees formed a vertical angle with the combined right angle and angle measuring x degrees.)
• “Does either method get us the same answer for both unknown angle measures?” (Yes.)

Explain to students that there might be multiple ways to get an answer because of the many angle relationships found in some figures. In the next activity, encourage them to look for different methods.

In this activity, students come up with equations that represent the relationships between angles in a figure. Then, students solve their equation to find each unknown angle measure.

If students struggle to see the angle relationships in the figures, consider asking:

• “What types of angle relationships do you see?”
• “How can those angle relationships help you find the unknown angle measure?”

The goal of this discussion is for students to see different equations that can be used to represent and solve for the same unknown angle measures.

Select students to share their answers to each problem. Consider asking some of the following questions:

• “Did anyone use a different equation for this same problem? If so, did you get the same answer?”
• “Were any of the questions harder than others? Why?”
• “Were there any questions for which you used a strategy that was new to you?”