Unit 7, Lesson 5
Using Equations to Solve for Unknown Angles
Grade 7
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In this activity, students consider whether there is enough information given to solve for the unknown angle measures. In previous lessons, students were given the measures of some angles in a figure and asked to solve for another. In this warm-up, the figure contains two unknowns and students are asked to critique Tyler’s thinking (MP3).
The discussion addresses the case in which angles
Arrange students in groups of 2. Give students 1 minute of quiet think time, followed by time to discuss their reasoning with their partner. Follow with a whole-class discussion.
Tyler thinks that this figure has enough information to figure out the values of
Do you agree? Explain your reasoning.
Invite students to share their reasoning until they reach an agreement that Tyler is incorrect.
Ask students to come up with an equation to represent the angle measures in the figure. (
Display this image. Invite students to share how this figure is the same as the figure from the task and how it is different.
If students do not mention any of these points, make sure to point them out:
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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).
Tell students that each diagram has two possible equations, and that their job is to choose the equation that best represents a relationship between angles in the diagram. Then they are to solve their chosen equation.
Keep students in the same groups. Give 5 minutes of quiet work time, followed by time to discuss reasoning with a partner. Follow with a whole-class discussion.
Tell students they can assume that the angles that appear to be right angles are 90 degrees. Students may also use an index card or corner of a piece of paper to identify any right angles, if needed.
Elena and Diego each wrote equations to represent these diagrams. For each diagram, decide which equation you agree with, and then solve it.
Elena:
Diego:
Elena:
Diego:
Elena:
Diego:
Elena:
Diego:
Elena:
Diego:
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:
For the last question, have students who used different equations to figure out the unknown angle measures share their explanations. Ask students:
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.
MLR8: Discussion Supports
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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.
Give students 2–3 minutes of quiet work time, followed by a whole-class discussion.
Monitor for students who represent their thinking using equations, and select these students to share during the whole-class discussion.
Find the unknown angle measures. Show your thinking. Organize it so it can be followed by others.
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:
To find an unknown angle measure, sometimes it is helpful to write and solve an equation that represents the situation. For example, suppose we want to know the value of
Using what we know about vertical angles, we can write the equation
Help us improve by sharing suggestions or reporting issues.
If students struggle to see the angle relationships in the figures, consider asking: