 # Solve for Unknown Angles

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Lesson Plans and Worksheets for Grade 7
Lesson Plans and Worksheets for all Grades

Videos, examples, lessons, and solutions to help Grade 7 students learn how to solve for unknown angles using equations in word problems and in diagrams involving complementary and supplementary angles.

### Lesson 1 Student Outcomes

• Students learn how to solve for unknown angles using equations.
• Students solve for unknown angles in word problems and in diagrams involving complementary and supplementary angles.

### Lesson 1 Summary

• To determine the measurement of an unknown angle, we must identify the angle relationship(s), and then model the relationship with an equation that will yield the unknown value.
• If the sum of the measurements of two angles is 90°, angles are complementary angles and one is the complement of the other.
• If the sum of the measurements of two angles is 180°, angles are supplementary angles and one is the supplement of the other.

Lesson 1 Classwork

Review key definitions: Adjacent, Vertical, Vertically opposite, Perpendicular.

Complete the missing information in the table below. In the ‘Statement’ column, use the illustration to write an equation that demonstrates the angle relationship; use all forms of angle notation in your equations. Adjacent angles, Vertical angles, Angles on a line, Angles at a point.

Discussion

Develop definitions for supplementary and complementary angle pairs.

Exercise 1
1. In a complete sentence, describe the relevant angle relationships 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.

Example 1
The measures of two supplementary angles are in the ratio of 2: 3. Find the two angles.

Exercises 2–4
2. In a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle.
Find the measurements of the two angles.
3. The measure of a supplement of an angle is 6° more than twice the measure of the angle. Find the two angles.
4. The measure of a complement of an angle is 32° more than three times the angle. Find the two angles.

Example 2
Two lines meet at the common vertex of two rays. Set up and solve an appropriate equation for x and y.

Example 1
The measures of two supplementary angles are in the ratio of 2: 3. Find the two angles.

Exercise 2:
In a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle.
Find the measurements of the two angles.

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