Solve Angle Problems and 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 10

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Lesson 10 Student Outcomes

• Students use vertical and adjacent angles and angles on a line and angles at a point in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Relevant Vocabulary
Adjacent Angles: Two angles ∠BAC and ∠CAD with a common side AC are adjacent angles if C belongs to the interior of ∠BAD.
Vertical Angles: Two angles are vertical angles (or vertically opposite angles) if their sides form two pairs of opposite rays.
Angles on a Line: The sum of the measures of adjacent angles on a line is 180°.
Angles at a Point: The sum of the measures of adjacent angles at a point is 360°.

Classwork
We can name an angle by naming the arc, by the vertex or three points.

Example 1
Estimate the measurement of x.
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. Then find the measures of ∠BAC and confirm your answers by measuring the angle with a protractor.

Exercise 1
In a complete sentence, describe the angle relationship in the diagram.
Find the measurements of ∠BAC and ∠DAE.

Example 2
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 and y. Find the measurements of ∠LEB and ∠KEB.

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.

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 measurement of ∠EKF and confirm your answers by measuring the angle with a protractor.

Exercise 3
In a complete sentence, describe the angle relationships in the diagram.
Find the measurement of ∠GAH.

Example 4
Two lines intersect in the following figure. In the figure, the ratio of the measurements of the obtuse angle to the acute angle in any adjacent angle pair is 2:1.
In a complete sentence, describe the angle relationships in the diagram. Label the diagram with expressions that describe this relationship. Write an equation that models the angle relationship and solve for x. Find the measurements of the acute and obtuse angles. Exercise 4 The ratio of ∠GFH to ∠EFH is 2:3. In a complete sentence, describe the angle relationships in the diagram. Find the measures of ∠GFH and ∠EFH.

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