# Lesson 4

Solving for Unknown Angles

### 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 Preparation

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

### 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.

Building Towards

### Glossary Entries

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.