Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Complementary and Supplementary Angles

Trigonometry

1. Measuring Angles

Complementary and Supplementary Angles

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2:36 minutes

Problem 18

Textbook Question

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Verified step by step guidance

Identify the given information: m and n are parallel lines, and there are marked angles formed by a transversal intersecting these lines.

Recall the properties of parallel lines and transversals: corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary.

Use the property of corresponding angles to find the measure of angles that are in the same relative position at each intersection of the transversal with the parallel lines.

Apply the property of alternate interior angles to find the measure of angles that are on opposite sides of the transversal but inside the parallel lines.

If needed, use the property of consecutive interior angles being supplementary to find any remaining angle measures by setting up an equation where the sum of the angles equals 180 degrees.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Parallel Lines and Transversals

When two lines are parallel, and a transversal crosses them, several angle relationships are formed. Corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. Understanding these relationships is crucial for solving problems involving parallel lines and angles.

Angle Relationships

In geometry, angles can be classified into various relationships such as complementary, supplementary, and vertical angles. Complementary angles sum to 90 degrees, while supplementary angles sum to 180 degrees. Vertical angles, formed by two intersecting lines, are always equal. Recognizing these relationships helps in calculating unknown angles.

Angle Measurement

Angle measurement is typically expressed in degrees or radians. In this context, understanding how to convert between these units and apply them in calculations is essential. Additionally, knowing how to use a protractor or apply geometric principles to find angle measures is fundamental in solving angle-related problems.