Lesson 5Using Equations to Solve for Unknown Angles
Learning Goal
Let’s figure out missing angles using equations.
Learning Targets
I can write an equation to represent a relationship between angle measures and solve the equation to find unknown angle measures.
Lesson Terms
- adjacent angles
- complementary
- right angle
- straight angle
- supplementary
- vertical angles
Warm Up: Is This Enough?
Problem 1
Tyler thinks that this figure has enough information to figure out the values of
Do you agree? Explain your reasoning.
Activity 1: What Does It Look Like?
Problem 1
Elena and Diego each wrote equations to represent these diagrams. For each diagram, decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.
Elena:
Diego:
Elena:
Diego:
Elena:
Diego:
Elena:
Diego:
Elena:
Diego:
Activity 2: Calculate the Measure
Problem 1
Find the unknown angle measures. Show your thinking. Organize it so it can be followed by others.
Are you ready for more?
Problem 1
The diagram contains three squares. Three additional segments have been drawn that connect corners of the squares. We want to find the exact value of
Use a protractor to measure the three angles. Use your measurements to conjecture about the value of
. Find the exact value of
by reasoning about the diagram.
Lesson Summary
To find an unknown angle measure, sometimes it is helpful to write and solve an equation that represents the situation. For example, suppose we want to know the value of
Using what we know about vertical angles, we can write the equation