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Transformations and Angle Relationships

Lesson 19


Solve for missing angle measures in parallel line diagrams using equations.

Common Core Standards

Core Standards


  • 8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Foundational Standards


  • 8.EE.C.7

  • 7.G.B.5

Criteria for Success


  1. Use angle relationships in parallel line diagrams to set up and solve equations.
  2. Know that in congruent relationships, expressions are equal to one another.
  3. Know that in supplementary or complementary relationships, expressions add up to equal either 180° or 90°, respectively.

Tips for Teachers


A common misunderstanding is to set up an incorrect equation, for example, setting the expressions equal to each other in a supplementary relationship. Have students start by looking at the structure of the diagram and understanding the relationship between the angles before they set up an equation (MP.7).

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

Fishtank Plus

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  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package


Anchor Problems


Problem 1

Lines $${L_1 }$$ and $${L_2}$$ are parallel and cut by transversal $$p$$.

What is the measure of the angles shown by the algebraic expressions?

Guiding Questions

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Problem 2

Determine the values of $$x$$ and $$y$$ in the diagram below, and use them to determine the measures of the eight angles formed by the parallel lines and transversal.

Guiding Questions

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Problem Set


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

  • Error analysis of incorrectly set up equations.

Target Task


Lines $$b$$ and $$c$$ are parallel cut by transversal line $$a$$. Determine all of the angle measures.

Mastery Response


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