Table of contents

0. Review of College Algebra4h 43m

Rationalizing Denominators
15m

Pythagorean Theorem & Basics of Triangles
17m

Basics of Graphing
30m

Functions
41m

Transformations
45m

Asymptotes
4m

Solving Linear Equations
31m

Solving Quadratic Equations
55m

Complex Numbers
41m

1. Measuring Angles40m

Angles in Standard Position
12m

Coterminal Angles
8m

Complementary and Supplementary Angles
10m

Radians
8m

2. Trigonometric Functions on Right Triangles2h 5m

Trigonometric Functions on Right Triangles
45m

Special Right Triangles
30m

Cofunctions of Complementary Angles
26m

Solving Right Triangles
23m

3. Unit Circle1h 19m

Defining the Unit Circle
14m

Trigonometric Functions on the Unit Circle
9m

Common Values of Sine, Cosine, & Tangent
11m

Reference Angles
38m

Reciprocal Trigonometric Functions on the Unit Circle
6m

4. Graphing Trigonometric Functions1h 19m

Graphs of the Sine and Cosine Functions
32m

Phase Shifts
14m

Graphs of Secant and Cosecant Functions
10m

Graphs of Tangent and Cotangent Functions
21m

5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m

Inverse Sine, Cosine, & Tangent
28m

Evaluate Composite Trig Functions
44m

Linear Trigonometric Equations
28m

6. Trigonometric Identities and More Equations2h 34m

Introduction to Trigonometric Identities
1h 4m

Sum and Difference Identities
1h 3m

Double Angle Identities
16m

Solving Trigonometric Equations Using Identities
9m

7. Non-Right Triangles1h 38m

Law of Sines
49m

Law of Cosines
30m

Area of SAS & ASA Triangles
19m

8. Vectors2h 25m

Geometric Vectors
28m

Vectors in Component Form
32m

Direction of a Vector
23m

Unit Vectors and i & j Notation
27m

Dot Product
22m

Cross Product
11m

9. Polar Equations2h 5m

Polar Coordinate System
29m

Convert Points Between Polar and Rectangular Coordinates
26m

Convert Equations Between Polar and Rectangular Forms
29m

Graphing Other Common Polar Equations
39m

10. Parametric Equations1h 6m

Graphing Parametric Equations
12m

Eliminate the Parameter
32m

Writing Parametric Equations
21m

11. Graphing Complex Numbers1h 7m

Graphing Complex Numbers
6m

Polar Form of Complex Numbers
22m

Products and Quotients of Complex Numbers
14m

Powers of Complex Numbers (DeMoivre's Theorem)
23m

1. Measuring Angles

Complementary and Supplementary Angles

Trigonometry

1. Measuring Angles

Complementary and Supplementary Angles

Previous problemNext problem

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

0 Comments

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.