Lesson 5

Using Equations to Solve for Unknown Angles

Lesson Narrative

In the previous lesson, students saw that equations could be used to represent relationships between angles. In this lesson, students practice writing and solving equations of the form \(px + q = r\) in the context of finding unknown angle measures. This brings together their work with equations from the previous unit and their work with angles from earlier lessons in this unit, giving students a chance to build fluency with both of these concepts.


Learning Goals

Teacher Facing

  • Critique whether a given equation represents the relationship between angles in a diagram.
  • Solve an equation that represents a relationship between angle measures, and explain (in writing and using other representations) the reasoning.
  • Write an equation of the form $px+q=r$ or $p(x+q)=r$ to represent the relationship between angles in a given diagram.

Student Facing

Let’s figure out missing angles using equations.

Learning Targets

Student Facing

  • I can write an equation to represent a relationship between angle measures and solve the equation to find unknown angle measures.

CCSS Standards

Building On

Addressing

Glossary Entries

  • adjacent angles

    Adjacent angles share a side and a vertex.

    In this diagram, angle \(ABC\) is adjacent to angle \(DBC\).

    Three segments all joined at endpoint B. Point A is to the left of B and segment A B is drawn. Point C is above B and segment C B is drawn. Point D is to the right of B and segment B D is drawn.
  • complementary

    Complementary angles have measures that add up to 90 degrees.

    For example, a \(15^\circ\) angle and a \(75^\circ\) angle are complementary.

    complementary angles of 15 and 75 degrees
    Two angles, one is 75 degrees and one is 15 degrees
  • right angle

    A right angle is half of a straight angle. It measures 90 degrees.

    a right angle
  • straight angle

    A straight angle is an angle that forms a straight line. It measures 180 degrees.

    a 180 degree angle
  • supplementary

    Supplementary angles have measures that add up to 180 degrees.

    For example, a \(15^\circ\) angle and a \(165^\circ\) angle are supplementary.

    supplementary angles of 15 and 165 degrees
    supplementary angles of 15 and 165 degrees
  • vertical angles

    Vertical angles are opposite angles that share the same vertex. They are formed by a pair of intersecting lines. Their angle measures are equal.

    For example, angles \(AEC\) and \(DEB\) are vertical angles. If angle \(AEC\) measures \(120^\circ\), then angle \(DEB\) must also measure \(120^\circ\).

    Angles \(AED\) and \(BEC\) are another pair of vertical angles.

    a pair of intersecting lines that create vertical angles

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