Lesson 4

Solving for Unknown Angles

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Lesson Narrative

In previous lessons, students solved single-step problems about supplementary, complementary, and vertical angles. In this lesson, students apply these skills to find unknown angle measures in multi-step problems. In the info gap activity, students keep asking questions until they get all the information needed to solve the problem. Then they see that they can represent angle problems with equations. As students work to construct arguments about angles and discuss them with their partners, they engage in MP3. 

Learning Goals

Teacher Facing

  • Coordinate (orally and in writing) diagrams and equations that represent the same relationship between angle measures.
  • Solve multi-step problems involving complementary, supplementary, and vertical angles, and explain (orally) the reasoning.

Student Facing

Let’s figure out some missing angles.

Required Materials

Required Preparation

Make 1 copy of the Info Gap: Angle Finding blackline master for every 2 students, and cut them up ahead of time.

Learning Targets

Student Facing

  • I can reason through multiple steps to find unknown angle measures.
  • I can recognize when an equation represents a relationship between angle measures.

CCSS Standards

Addressing

Building Towards

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