# 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 complementary, supplementary, vertical, and adjacent angles.

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Lesson Plans and Worksheets for Grade 7

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## New York State Common Core Math Grade 7, Module 6, Lesson 2

### Lesson 2 Student Outcomes

• Students solve for unknown angles in word problems and in diagrams involving complementary, supplementary, vertical, and adjacent angles.

### Lesson 2 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 2 Classwork

Opening Exercise
Two lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Find the values of r, s, and t.

Example 1
Two lines meet at the vertex of a ray. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of p and r.

Exercise 1
Three lines meet at a point. In a complete sentence, describe the relevant angle relationship in the diagram. Set up and solve an equation to find the value of a.

Example 2
Three lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of z.

Exercise 2
Three lines meet at a point; angle AOF = 144°. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to determine the value of c.

Example 3
Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of t.

Exercise 3
Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. In a complete sentence, describe the relevant angle relationships in the diagram. You may add labels to the diagram to help with your description of the angle relationship. Set up and solve an equation to find the value of v.

Example 4
Three lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Is your answer reasonable? Explain how you know.

Exercise 4
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 angle AOB and angle BOC.

Exercise 5
a. 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 angle AOB and angle BOC.
b. Katrina was solving the problem above and wrote the equation 7x + 20 = 90. Then she rewrote this as 7x + 20 = 70 + 20. Why did she rewrite the equation in this way? How does this help her to find the value of x?

Lesson 2 Problem Set Sample Solutions

1. Two lines meet at the vertex of a ray. Set up and solve an equation to find the value of c.

3. Two lines meet at the vertex of a ray. Set up and solve an equation to find the value of w.

5. Three lines meet at a point. Set up and solve an equation to find the value of r.

7. Set up and solve an equation to find the value of x. Find the measurement of angle AOB and of angle BOC.

9. Set up and solve an equation to find the value of x. Find the measurement of angle AOB and of angle BOC.