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: minutes

Problem 23

Textbook Question

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 37° , 52°

Verified step by step guidance

Identify that the sum of the angles in a triangle is always 180°.

Add the measures of the two given angles: 37° + 52°.

Subtract the sum of the two angles from 180° to find the measure of the third angle.

Set up the equation: 180° - (37° + 52°) = third angle.

Solve the equation to find the measure of the third angle.

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Key Concepts

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

Triangle Angle Sum Theorem

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. This fundamental principle allows us to determine the measure of an unknown angle when the measures of the other two angles are known. For example, if two angles measure 37° and 52°, we can find the third angle by subtracting their sum from 180°.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. While this concept is not directly applicable to finding the third angle in a triangle, understanding complementary angles can help in various trigonometric problems. In the context of triangles, it is important to distinguish between complementary angles and the angles that sum to 180 degrees.

Angle Measurement

Angle measurement is the process of determining the size of an angle in degrees or radians. In this problem, angles are given in degrees, which is a common unit for measuring angles in trigonometry. Understanding how to convert between degrees and radians, as well as how to manipulate angle measures, is essential for solving problems involving triangles and other geometric figures.