Angle Problems and Solving Equations

Examples, videos, and solutions to help Grade 7 students learn how to use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem write and solve simple equations for an unknown angle in a figure.

New York State Common Core Math Grade 7, Module 3, Lesson 11

Download worksheets for Grade 7, Module 3, Lesson 11

Lesson 11 Student Outcomes

• Students use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Lesson 11 Classwork
Opening Exercise
a. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Confirm your answers by measuring the angle with a protractor.
b. CD and EF are intersecting lines. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for . Confirm your answers by measuring the angle with a protractor.
c. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for y. Confirm your answers by measuring the angle with a protractor.
d. The following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for z. Confirm your answers by measuring the angle with a protractor.
e. Write an equation for the angle relationship shown in the figure and solve for x. In a complete sentence, describe the angle relationship in the diagram. Find the measurements of EPB and CPA. Confirm your answers by measuring the angle with a protractor.

Example 1
The following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Confirm your answers by measuring the angle with a protractor.

Exercise 1
The following figure shows four lines intersecting at a point. In a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x and y. Confirm your answers by measuring the angle with a protractor.

Example 2
In a complete sentence, describe the angle relationships in the diagram. You may label the diagram to help describe the angle relationships. Write an equation for the angle relationship shown in the figure and solve for x. Confirm your answers by measuring the angle with a protractor.

Exercise 2
In a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x and y. Confirm your answers by measuring the angle with a protractor.

Example 3
In a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Find the measures of JAH and GAF. Confirm your answers by measuring the angle with a protractor.

Exercise 3
In a complete sentence, describe the angle relationships in the diagram. Write an equation for the angle relationship shown in the figure and solve for x. Find the measure of JKG. Confirm your answers by measuring the angle with a protractor.

Example 4
In the accompanying diagram, DBE is four times the measure of FBG.
a. Label DBE as y° and FBG as x°. Write an equation that describes the relationship between DBE and FBG
b. Find the value of x.
c. Find the measures of FBG, CBD, ABF, GBE, DBE.
d. What is the measure of ABG? Identify the angle relationship used to get your answer.

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