Lesson 4
Solving for Unknown Angles
Lesson Narrative
In previous lessons, students solved singlestep problems about supplementary, complementary, and vertical angles. In this lesson, students apply these skills to find unknown angle measures in multistep 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 multistep 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.
Glossary Entries

adjacent angles
Adjacent angles share a side and a vertex.
In this diagram, angle \(ABC\) is adjacent to angle \(DBC\).

complementary
Complementary angles have measures that add up to 90 degrees.
For example, a \(15^\circ\) angle and a \(75^\circ\) angle are complementary.

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

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

supplementary
Supplementary angles have measures that add up to 180 degrees.
For example, a \(15^\circ\) angle and a \(165^\circ\) angle are supplementary.

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.