Angle Problems and Solving Equations Problem Set

For each question, use angle relationships to write an equation in order to solve for each variable. Determine the indicated angles. You can check your answers by measuring each angle with a protractor.

1. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measurement

of∠𝐷𝐷𝐵𝐵𝐷𝐷.

2. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measurement of ∠𝑄𝑄𝑄𝑄𝑄𝑄.

3. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measurements

of ∠𝐵𝐵𝑄𝑄𝐷𝐷 and ∠𝐷𝐷𝑄𝑄𝐸𝐸.

4. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measure of𝑥𝑥.

A STORY OF RATIOS

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Lesson 10

Lesson 10: Angle Problems and Solving Equations

5. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measures of𝑥𝑥

and 𝑦𝑦.

6. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measures of𝑥𝑥

and 𝑦𝑦.

7. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measures

of∠𝐵𝐵𝐵𝐵𝐷𝐷 and ∠𝐷𝐷𝐵𝐵𝐷𝐷.

A STORY OF RATIOS

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Lesson 10

Lesson 10: Angle Problems and Solving Equations

8. In a complete sentence, describe the relevant angle relationships in the following diagram. Find the measure of

∠𝐵𝐵𝑄𝑄𝐺𝐺.

9. The ratio of the measures of a pair of adjacent angles on a line is 4∶5. a. Find the measures of the two angles.

b. Draw a diagram to scale of these adjacent angles. Indicate the measurements of each angle.

10. The ratio of the measures of three adjacent angles on a line is 3∶4∶5. a. Find the measures of the three angles.

b. Draw a diagram to scale of these adjacent angles. Indicate the measurements of each angle. A STORY OF RATIOS

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Lesson 11

Lesson 11: Angle Problems and Solving Equations

Lesson 11: Angle Problems and Solving Equations

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 𝑥𝑥. Confirm your answers by measuring the angle with a protractor.

b. ⃖����⃗𝐶𝐶𝐶𝐶 and 𝐸𝐸𝐸𝐸⃖����⃗ 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 𝑦𝑦. Confirm your answers by measuring the angle with a protractor.

A STORY OF RATIOS

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Lesson 11

Lesson 11: Angle Problems and Solving Equations

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 for𝑏𝑏. 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 𝑧𝑧. 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 𝑥𝑥. In a complete sentence, describe the angle relationship in the diagram. Find the measurements of ∠𝐸𝐸𝐸𝐸𝐸𝐸 and ∠𝐶𝐶𝐸𝐸𝐶𝐶. Confirm your answers by measuring the angle with a protractor.

A STORY OF RATIOS

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Lesson 11

Lesson 11: Angle Problems and Solving Equations

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 𝑥𝑥. 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 𝑥𝑥 and 𝑦𝑦. 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 𝑥𝑥. Confirm your answers by measuring the angle with a protractor.

A STORY OF RATIOS

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Lesson 11

Lesson 11: Angle Problems and Solving Equations

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 𝑥𝑥 and 𝑦𝑦. Confirm your answers by measuring the angles 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 𝑥𝑥. Find the measures of ∠𝐽𝐽𝐶𝐶𝐽𝐽 and ∠𝐺𝐺𝐶𝐶𝐸𝐸. 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 𝑥𝑥. Find the measures of ∠𝐽𝐽𝐽𝐽𝐺𝐺. Confirm your answer by measuring the angle with a protractor.

A STORY OF RATIOS

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Lesson 11

Lesson 11: Angle Problems and Solving Equations

Example 4

In the accompanying diagram, the measure of ∠𝐶𝐶𝐸𝐸𝐸𝐸 is four times the measure of ∠𝐸𝐸𝐸𝐸𝐺𝐺. a. Label ∠𝐶𝐶𝐸𝐸𝐸𝐸 as 𝑦𝑦° and ∠𝐸𝐸𝐸𝐸𝐺𝐺as 𝑥𝑥°. Write an equation that

describes the relationship between ∠𝐶𝐶𝐸𝐸𝐸𝐸 and ∠𝐸𝐸𝐸𝐸𝐺𝐺.

b. Find the value of 𝑥𝑥.

c. Find the measures of ∠𝐸𝐸𝐸𝐸𝐺𝐺, ∠𝐶𝐶𝐸𝐸𝐶𝐶, ∠𝐶𝐶𝐸𝐸𝐸𝐸, ∠𝐺𝐺𝐸𝐸𝐸𝐸, and ∠𝐶𝐶𝐸𝐸𝐸𝐸.

d. What is the measure of ∠𝐶𝐶𝐸𝐸𝐺𝐺? Identify the angle relationship used to get your answer. A STORY OF RATIOS

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Lesson 11

Lesson 11: Angle Problems and Solving Equations

Problem Set

In a complete sentence, describe the angle relationships in each diagram. Write an equation for the angle relationship(s) shown in the figure, and solve for the indicated unknown angle. You can check your answers by measuring each angle with a protractor.

1. Find the measures of∠𝐸𝐸𝐶𝐶𝐸𝐸, ∠𝐶𝐶𝐶𝐶𝐸𝐸, and ∠𝐶𝐶𝐶𝐶𝐶𝐶.

2. Find the measure of 𝑎𝑎.

3. Find the measures of 𝑥𝑥 and 𝑦𝑦. A STORY OF RATIOS

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Lesson 11

Lesson 11: Angle Problems and Solving Equations