 # Solve for Unknown Angles using Equations

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Examples, videos, and solutions to help Grade 7 students learn how to solve for unknown angles in word problems and in diagrams involving all learned angle facts.

### New York State Common Core Math Grade 7, Module 6, Lesson 3

Download worksheets for Grade 7, Module 6, Lesson 3

### Lesson 3 Student Outcomes

• Students solve for unknown angles in word problems and in diagrams involving all learned angle facts.

### Lesson 3 Summary

• In every unknown angle problem, it is important to identify the angle relationship(s) correctly in order to set up an equation that will yield the unknown value.
• Check your answer by substituting and/or measuring to be sure it is correct.

Lesson 3 Classwork

Opening Exercise
Two lines meet at the common vertex of two rays; the measurement of angle COF = 134°. Set up and solve an equation to find the value of x and y. Are your answers reasonable? How do you know?

Example 1 Set up and solve an equation to find the value of x.

Exercise 1
Five rays meet at a common vertex. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of a.

Example 2
Four rays meet at a common vertex. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurements of angles BAC and DAE.

Exercise 2
Four rays meet at a common vertex. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurement of angle CAD.

Example 3
Two lines meet at the common vertex of two rays. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurements of angles BAC and BAH.

Exercise 3
Two lines meet at the common vertex of two rays. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurements of angles DHF and AHD.

Example 4
Two lines meet at a point. Set up and solve an equation to find the value of x. Find the measurement of one of the vertical angles.

Exercise 4
Set up and solve an equation to find the value of x. Find the measurement of one of the vertical angles.

Lesson 3 Problem Set Sample Solutions

1. Two lines meet at a point. Set up and solve an equation to find the value of x.

2. Three lines meet at a point. Set up and solve an equation to find the value of a. Is your answer reasonable? Explain how you know.

3. Two lines meet at the common vertex of two rays. Set up and solve an equation to find the values of a and b.

4. Two lines meet at the common vertex of two rays. Set up and solve an equation to find the values of x and y.

10. Solve for x and y in the following diagram.

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