Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*DaQuita Hester*

DaQuita has taught high school mathematics for six years and has a master's degree in secondary mathematics education.

Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.

In another lesson, we learned about the different types of angles: consecutive interior, alternate interior, alternate exterior and corresponding. We discovered that when two lines are parallel, all of the angle pairs are congruent, except for consecutive interior angles, which are supplementary. We also learned about vertical angles, which are always congruent. Let's do some practice with these angles.

In the figure below, let *Angle 5* = 30*y* + 31, and let *Angle 9* = 22*y* + 55. What is the value of *y*?

*Angle 5* and *Angle 9* don't match any of the angle pairs, so let's find the connection between their measures. We notice that *Angle 5* corresponds to *Angle 1*, and *Angle 1* corresponds to *Angle 9*. Knowing that all corresponding angles are congruent, *Angle 5* = *Angle 1*, and *Angle 1* = *Angle 9*. So, by the transitive property of equality, we can conclude that *Angle 5* = *Angle 9*. By substituting the equations, we have 30*y* + 31 = 22*y* + 55. From here, we can subtract 31 from both sides to get 30*y* = 22*y* + 24, and then subtract 22*y* from each side to get 8*y* = 24. To finish, we will divide both sides by 8 to determine that *y* = 3.

Let's do another using the same figure. This time, let *Angle 4* = 14*x* - 23, and let *Angle 14* = 4*x* + 5. Find the measure of *Angle 15*.

Once again, these angles are not a special angle pair; so, let's find the connection. *Angle 4* corresponds to *Angle 12*, and *Angle 12* is consecutive interior to *Angle 14*. Therefore, *Angle 4* = *Angle 12*, and *Angle 12* + *Angle 14* = 180. With this knowledge, we can replace *Angle 12* with *Angle 4* to get *Angle 4* + *Angle 14* = 180. With the equations, we have 14*x* - 23 + 4*x* + 5 = 180. Combining like terms gives us 18*x* - 18 = 180, and then, by adding 18 to both sides, we get 18*x* = 198. Last, we will divide both sides by 18 to conclude that *x* = 11.

Now we can find the value of *Angle 15*, which is vertical to and congruent with *Angle 14*. Substituting 11 into the equation, we see that *Angle 14* = 4(11) + 5, which equals 49. Therefore, we can also conclude that *Angle 15* = 49 degrees.

When working with triangles, remember that the sum of all three angles in every triangle is 180 degrees. Let's get started.

In this first triangle below, let's solve for *x*.

For each angle, we either have a measure or an equation. For that reason, let's add all of the angles together to equal 180 degrees. Doing so, we have 40 + 10*x* + 20 + 20 = 180, and by combining like terms, we have 10*x* + 80 = 180. Next, let's subtract 80 from both sides to get 10*x* = 100, and then let's divide each side by 10 to finish with *x* = 10.

Here's another. This is triangle *JKL*. What is the measure of *Angle L*?

By having information for all three angles, we will add them together to equal 180. Remember that the square in the angle tells us that the angle measures 90 degrees. So, we can begin with 10*y* + 5 + 90 + 15*y* + 35 = 180. Combining like terms gives us 25*y* + 130 = 180. From here, we will subtract 130 from both sides, leaving 25*y* = 50. Then, let's divide both sides by 25 to see that *y* = 2. Now, by substitution, we see that *Angle L* = 15(2) + 35, which equals 65 degrees.

Let's do one more. In triangle *DEF* below, *Angle D* is two times a number, *Angle E* is forty more than five times the number, and *Angle F* is five more than two times the number. What is the measure of *Angle E*?

Since we don't have the exact equation for each angle, we have to use the descriptions to create them. All of the descriptions reference some unknown number. Not knowing what this number is, we will call it *x* in each equation. Therefore, *Angle D* = 2*x*, *Angle E* = 5*x* + 40, and *Angle F* = 2*x* + 5.

To solve, we begin with 2*x* + 5*x* + 40 + 2*x* + 5 = 180. Combining like terms gives us 9*x* + 45 = 180, and then subtracting 45 from both sides leaves us with 9*x* = 135. From here, we will divide both sides by 9 to get *x* = 15. To complete the problem, we will substitute 15 into the equation for *Angle E* to see that *Angle E* = 5(15) + 40, which equals 115 degrees.

In review, when solving with angles and lines, always begin by determining the special angle pair or the connection between the angles you were given. This will send you in the right direction for determining whether you should set the angles equal to each other or add them together to equal 180 degrees. But remember, to solve these problems in this manner, the two lines must be parallel.

When it comes to triangles, remember that all of the angles in every triangle must add together to equal 180 degrees. So, when you have information for each angle in a triangle, this is the best way to start and solve the problem.

After completing this lesson, you'll be able to:

- Solve for angles using the rules for consecutive interior, alternate interior, alternate exterior and corresponding angles
- Calculate an angle of a triangle when given some information about all three angles

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
11 in chapter 14 of the course:

Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

- Go to Logic

- Go to Sets

- Properties of Shapes: Rectangles, Squares and Rhombuses 5:46
- Properties of Shapes: Triangles 5:09
- Perimeter of Triangles and Rectangles 8:54
- Area of Triangles and Rectangles 5:43
- Circles: Area and Circumference 8:21
- The Pythagorean Theorem: Practice and Application 7:33
- How to Identify Similar Triangles 7:23
- Applications of Similar Triangles 6:23
- Parallel, Perpendicular and Transverse Lines 6:06
- Types of Angles: Vertical, Corresponding, Alternate Interior & Others 10:28
- Angles and Triangles: Practice Problems 7:43
- Go to Geometry

- Trauma Certified Registered Nurse (TCRN): Study Guide
- English 310: Short Stories
- Nurse Entrance Test (NET): Exam Prep & Study Guide
- CCMA Basic Exam: Study Guide & Test Prep
- Personalized Learning in the Classroom
- Diseases of the Central Nervous System
- TOEFL Vocabulary: Words & Practice
- SAT Vocabulary Practice
- Patient Assessments for Trauma Nurses
- Test-Taking Strategies for Reading Comprehension
- Professional Publications in Literacy
- Dyslexia Programs in Texas
- Study.com's Teacher Edition
- Study.com School Plans
- Study.com's Virtual Classrooms
- How to Set Up a Class and Invite Students in Your Study.com Virtual Classroom
- How to View Grades and Export CSVs in Your Study.com Virtual Classroom

- Implied Powers of Congress: Definition & Examples
- Brief History of Germany
- Biological Contamination of Food
- Emerging Technologies in Nursing
- Hubert Humphrey: Presidential Campaign & Platform
- How to Write & Use a Technical Specification Document
- Worcester v. Georgia: Lesson for Kids
- Common Characteristics of Fingerprints
- L.S. Lowry: Quiz & Worksheet for Kids
- Quiz & Worksheet - Korean Folklore & Deities
- Quiz & Worksheet - Graphing & Solving Systems of Inequalities
- Quiz & Worksheet - Calculating Markdown & Discount Pricing
- Quiz & Worksheet - Data Quality in Healthcare
- Developing Presentation Skills Flashcards
- Hypothesis Testing in Statistics Flashcards

- Introduction to Business: Certificate Program
- Linear Algebra: Tutoring Solution
- Information Systems for Teachers: Professional Development
- NMTA Essential Academic Skills Subtest Math: Practice & Study Guide
- Business Law: Skills Development & Training
- Human Body Systems
- Praxis Biology & General Science: Human Genetics
- Quiz & Worksheet - US Women's Movement of the 1960s
- Quiz & Worksheet - Calculating Integrals of Trigonometric Functions
- Quiz & Worksheet - Mood Disorders
- Quiz & Worksheet - Muscles of the Vertebral Column
- Quiz & Worksheet - Psychological Experiments & Ethics

- Exponentials, Logarithms & the Natural Log
- Frankfurt School: Critical Theory & Philosophy
- MCAT Tips
- How to Prepare for College
- Opportunity Cost Lesson Plan
- Transcontinental Railroad Lesson Plan
- How Hard is the CSET English?
- Short Story Lesson Plan
- Learning Computer Science Online
- Companies That Offer Tuition Reimbursement
- Finding GRE Test Centers and Dates
- What Classes Can You CLEP Out Of?

Browse by subject