Writing and Solving Linear Equations

Examples, videos, and solutions to help Grade 8 students apply knowledge of geometry to writing and solving linear equations.

New York State Common Core Math Grade 8, Module 4, Lesson 5

Worksheets for Grade 8

Lesson 5 Student Outcomes

• Students apply knowledge of geometry to writing and solving linear equations.

Lesson 5 Summary
• We know that an algebraic method for solving equations is more efficient than guessing and checking.
• We know how to write and solve equations that relate to angles, triangles, and geometry in general.
• We know that drawing a diagram can sometimes make it easier to understand a problem and that there is more than one way to solve an equation.

Classwork
Example 1
One angle is five less than three times the size of another angle. Together they have a sum of 143°. What are the sizes of each angle?

Example 2
Given a right triangle, find the size of the angles if one angle is ten more than four times the other angle and the third angle is the right angle.

Example 3
A pair of alternate interior angles are described as follows. One angle is fourteen more than half a number. The other angle is six less than half a number. Are the angles congruent?

Exercises 1–6
For each of the following problems, write an equation and solve.
1. A pair of congruent angles are described as follows: the measure of one angle is three more than twice a number and the other angle’s measure is 54.5 less than three times the number. Determine the size of the angles.

2. The measure of one angle is described as twelve more than four times a number. Its supplement is twice as large. Find the measure of each angle.

3. A triangle has angles described as follows: the first angle is four more than seven times a number, another angle is four less than the first and the third angle is twice as large as the first. What are the sizes of each of the angles?

4. One angle measures nine more than six times a number. A sequence of rigid motions maps the angle onto another angle that is described as being thirty less than nine times the number. What is the measure of the angles?

5. A right triangle is described as having an angle of size “six less than negative two times a number,” another angle that is “three less than negative one-fourth the number”, and a right angle. What are the measures of the angles?

6. One angle is one less than six times the size of another. The two angles are complementary angles. Find the size of each angle.

For each of the following problems, write an equation and solve.
1. The measure of one angle is thirteen less than five times the measure of another angle. The sum of the measures of the two angles is 140°. Determine the measures of each of the angles.
2. An angle measures seventeen more than three times a number. Its supplement is three more than seven times the number. What is the measure of each angle?
3. The angles of a triangle are described as follows: ∠A is the largest angle, its measure is twice the measure of ∠B. The measure of ∠C is less than half the measure of ∠B. Find the measures of the three angles.
4. A pair of corresponding angles are described as follows: the measure of one angle is five less than seven times a number and the measure of the other angle is eight more than seven times the number. Are the angles congruent? Why or why not?
5. The measure of one angle is eleven more than four times a number. Another angle is twice the first angle’s measure. The sum of the measures of the angles is 195°. What is the measure of each angle?
measure. The sum of the measures of the angles is 195°. What is the measure of each angle?
6. Three angles are described as follows: ∠B is half the size of ∠A. The measure of ∠C is equal to one less than times the measure of ∠B. The sum of ∠A and ∠B is 114. Can the three angles form a triangle? Why or why not?

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