# 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.

### Student Facing

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

Building On

### 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.