Geometry

Lesson 3

Math

Unit 6

7th Grade

Lesson 3 of 21

Objective


Use equations to solve for unknown angles. (Part 1)

Common Core Standards


Core Standards

  • 7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Foundational Standards

  • 4.MD.C.5
  • 4.MD.C.7

Criteria for Success


  1. Identify angle relationships in angle diagrams involving vertical, supplementary, and complementary angles.
  2. Write equations to represent relationships between known and unknown angle measurements. 
  3. Determine the measures of unknown angles and judge the reasonableness of the measures. 

Tips for Teachers


  • Lessons 3 and 4 present students with more complicated line and angle diagrams where they use various relationships between the angles to set up equations and solve for unknown angle measurements. The Guiding Questions ask students to observe and describe angle relationships they see in the diagrams first. This supports students in making sense of the diagrams and seeking a possible entry point before jumping in (MP.1). 
  • Some students may struggle with identifying the relevant relationships and setting up a corresponding equation; others may struggle with solving the equations. Keep an eye out for both/either struggles in order to provide targeted support.
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Anchor Problems


Problem 1

Three lines intersect at a point, as shown in the diagram below. 

Write and solve an equation to find the value of $$x$$

Guiding Questions

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Problem 2

Angle $${ABE}$$ below measures 146°. 

Write and solve equations to determine the values of $$x$$ and $$y$$.

Guiding Questions

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Problem 3

Two rays meet at a point that is also the vertex of an angle.

Set up and solve an equation to find the value of $$x$$. Explain why your answer is reasonable. 

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 6 > Topic A > Lesson 2Exit Ticket

Grade 7 Mathematics > Module 6 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 4

Two lines meet at a point that is also a vertex of an angle; the measurement of $${\angle AOF}$$ is 134°. 

Set up and solve an equation to find the values of $$x$$ and $$y$$.  

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 6 > Topic A > Lesson 3Opening Exercise

Grade 7 Mathematics > Module 6 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem Set

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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Two lines intersect at a point that is also a vertex of an angle. 

Write and solve equations to determine the values of $$x$$ and $$y$$.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Angle Relationships

Topic B: Circles

Topic C: Building Polygons and Triangles

Topic D: Solid Figures

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