This Math Talk focuses on angle measures of intersecting lines. It encourages students to think about angle relationships and to rely on what they know about straight angles to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students explain why vertical angles are congruent.

In this activity, students have an opportunity to notice and make use of structure (MP7) when they identify supplementary angles.

To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone use the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

The purpose of this activity is for students to generate an informal conjecture and study how to describe it more precisely by labeling a figure. Students begin by describing three examples of angle bisectors and forming a conjecture. By engaging with this explicit prompt to take a step back and become familiar with a context and the mathematics that might be involved, students are making sense of problems (MP1).

In this partner activity, students take turns describing the reasoning of the characters in the scenario. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

The purpose of this activity is for students to prove that vertical angles are congruent and work towards a more formal, rigorous way of expressing their arguments. As students work, remind them to label points and make markings on the diagram to help in the process of explaining their ideas.