# Solve for Unknown Angles using Equations

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

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Common Core For Grade 7

## New York State Common Core Math Grade 7, Module 6, Lesson 4

### Lesson 4 Student Outcomes

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

### Lesson 4 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 4 Classwork

Opening Exercise
Four times the measurement of an angle is the complement of the angle. Find the measurement of the angle and its complement.

Example 1
Find the measurement of FAE and CAD.
Two lines meet at a point. List the relevant angle relationship in the diagram. Set up and solve an equation to find the value of x. Find the measurement of one of the vertical angles.

Exercise 1
Set up and solve an equation to find the value of x. List the relevant angle relationship in the diagram. Find the measurement of one of the vertical angles.

Example 2
Three lines meet at a point. List the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x.

Exercise 2
Two lines meet at the common vertex of two rays. List the relevant angle relationships in the diagram. Set up and solve an equation to find the value of b.

Example 3
The measurement of an angle is 2/3 the measurement of its supplement. Find the measurement of the angle.

Exercise 3
The measurement of an angle is 1/4 the measurement of its complement. Find the measurement of the angle.

Example 4
Three lines meet at the common vertex of a ray. List the relevant angle relationships in the diagram. Set up and solve an equation to find the value of z.

Exercise 4
Two lines meet at the common vertex of two rays. Set up and solve an equation to find the value of x. Find the measurement of GAF and of BAC.

Lesson 4 Problem Set Sample Solutions

1. Four rays have a common vertex on a line. Set up and solve an equation to find the value of c

2. Lines BC and EF meet at A. Set up and solve an equation to find the value of x. Find the measurements of angle EAH and angle HAC.

3. Five rays meet at a point. Set up and solve an equation to find the values of x. Find the measurements of angle DAG and angle GAH.

6. Three angles are at a point. The second angle is 20 degrees more than the first, and the third angle is 20 degrees more than the second. Find the measurements of all three angles.

9. 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.

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