6.1.9 practice written assignment

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UMGC Effective Writing Center Designing an Effective Thesis

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Key Concepts

• A thesis is a simple sentence that combines your topic and your position on the topic.
• A thesis provides a roadmap to what follows in the paper.
• A thesis is like a wheel's hub--everything revolves around it and is attached to it.

After your prewriting activities-- such as assignment analysis and outlining--you should be ready to take the next step: writing a thesis statement. Although some of your assignments will provide a focus for you, it is still important for your college career and especially for your professional career to be able to state a satisfactory controlling idea or thesis that unifies your thoughts and materials for the reader.

Characteristics of an Effective Thesis

A thesis consists of two main parts: your overall topic and your position on that topic. Here are some example thesis statements that combine topic and position:

Sample Thesis Statements

Importance of tone.

Tone is established in the wording of your thesis, which should match the characteristics of your audience. For example, if you are a concerned citizen proposing a new law to your city's board of supervisors about drunk driving, you would not want to write this:

“It’s time to get the filthy drunks off the street and from behind the wheel: I demand that you pass a mandatory five-year license suspension for every drunk who gets caught driving. Do unto them before they do unto us!”

However, if you’re speaking at a concerned citizen’s meeting and you’re trying to rally voter support, such emotional language could help motivate your audience.

Using Your Thesis to Map Your Paper for the Reader

In academic writing, the thesis statement is often used to signal the paper's overall structure to the reader. An effective thesis allows the reader to predict what will be encountered in the support paragraphs. Here are some examples:

Use the Thesis to Map

Three potential problems to avoid.

Because your thesis is the hub of your essay, it has to be strong and effective. Here are three common pitfalls to avoid:

1. Don’t confuse an announcement with a thesis.

In an announcement, the writer declares personal intentions about the paper instead stating a thesis with clear point of view or position:

Write a Thesis, Not an Announcement

 2. a statement of fact does not provide a point of view and is not a thesis..

An introduction needs a strong, clear position statement. Without one, it will be hard for you to develop your paper with relevant arguments and evidence.

Don't Confuse a Fact with a Thesis

3. avoid overly broad thesis statements.

Broad statements contain vague, general terms that do not provide a clear focus for the essay.

Use the Thesis to Provide Focus

Practice writing an effective thesis.

OK. Time to write a thesis for your paper. What is your topic? What is your position on that topic? State both clearly in a thesis sentence that helps to map your response for the reader.

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AP CSA Java Course ¶

Welcome to CSAwesome! It’s time to start your journey to learn how to program with Java. A shortcut way to get to this site is to type in the url: course.csawesome.org

CSAwesome is a College Board endorsed curriculum for AP Computer Science A, an introductory college-level computer programming course in Java. If you are a teacher using this curriculum, please join the teaching CSAwesome group which will give you access to teacher resources at csawesome.org .

To make sure the site saves your answers on questions, please click on the person icon at the top to register or login to your Runestone course. As you complete lessons, click the “Mark as completed” button at the bottom. Enjoy the journey!

ATTENTION high school women of color taking AP CSA or CSP: if you identify as female and as Black, Hispanic/Latina, and/or Native American, apply to participate in Sisters Rise Up . The goal of Sisters Rise Up is to help you succeed in your AP Computer Science course and on the exam. They offer one-hour help sessions several times a week and once a month special help sessions often with guest speakers from computing. If you enroll in Sisters Rise Up and send in your AP CS exam score by the end of August, you will be sent a gift card for $100. See the flyer and apply at https://tinyurl.com/55z7tyb9 .

CSAwesome Units:

Table of Contents ¶

• 1.1.1. Preface
• 1.1.2. About the AP CSA Exam
• 1.1.3. Transitioning from AP CSP to AP CSA
• 1.1.4. Java Development Environments
• 1.1.5. Growth Mindset and Pair Programming
• 1.1.6. Pretest for the AP CSA Exam
• 1.1.7. Survey
• 1.2.1. First Java Program
• 1.2.2. Print Methods
• 1.2.3. Syntax Errors and Debugging
• 1.2.4. Reading Error Messages
• 1.2.5. Comments
• 1.2.6. Debugging Challenge
• 1.2.7. Summary
• 1.2.8. AP Practice
• 1.3.1. What is a Variable?
• 1.3.2. Data Types
• 1.3.3. Declaring Variables in Java
• 1.3.4. Naming Variables
• 1.3.5. Debugging Challenge : Weather Report
• 1.3.6. Summary
• 1.3.7. AP Practice
• 1.4.1. Assignment Statements
• 1.4.2. Adding 1 to a Variable
• 1.4.3. Input with Variables
• 1.4.4. Operators
• 1.4.5. The Remainder Operator
• 1.4.6. Programming Challenge : Dog Years
• 1.4.7. Summary
• 1.4.8. AP Practice
• 1.5.1. Code Tracing Challenge and Operators Maze
• 1.5.2. Summary
• 1.6.1. Programming Challenge : Average 3 Numbers
• 1.6.2. Bonus Challenge : Unicode
• 1.6.3. Summary
• 1.7.1. Concept Summary
• 1.7.2. Java Keyword Summary
• 1.7.3. Vocabulary Practice
• 1.7.4. Common Mistakes
• 1.8. Mixed Up Code Practice
• 1.9. Toggle Mixed Up or Write Code Practice
• 1.10. Coding Practice
• 1.11. Multiple Choice Exercises
• 2.1.1. What are Objects and Classes?
• 2.1.2. Intro to Objects with Turtles
• 2.1.3. Creating Turtle Objects
• 2.1.4. Programming Challenge : Turtle Drawing
• 2.1.5. Summary
• 2.1.6. AP Practice
• 2.2.1. Overloading Constructors
• 2.2.2. The World Class Constructors
• 2.2.3. The Turtle Class Constructors
• 2.2.4. Object Variables and References
• 2.2.5. Constructor Signatures
• 2.2.6. Formal and Actual Parameters
• 2.2.7. Programming Challenge: Custom Turtles
• 2.2.8. Summary
• 2.2.9. AP Practice
• 2.3.1. Procedural Abstraction
• 2.3.2. Programming Challenge : Draw a Letter
• 2.3.3. Summary
• 2.3.4. AP Practice
• 2.4.1. Tracing Methods
• 2.4.2. Programming Challenge : Turtle House
• 2.4.3. Summary
• 2.4.4. AP Practice
• 2.5.1. Accessors / Getters
• 2.5.2. Methods with Arguments and a Return Value
• 2.5.3. Programming Challenge : Turtle Distances
• 2.5.4. Summary
• 2.5.5. AP Practice
• 2.6.1. String Operators - Concatenation
• 2.6.2. Programming Challenge : Mad Libs
• 2.6.3. Summary
• 2.7.1. String Methods: length, substring, indexOf
• 2.7.2. CompareTo and Equals
• 2.7.3. Common Mistakes with Strings
• 2.7.4. Programming Challenge : Pig Latin
• 2.7.5. Summary
• 2.7.6. String Methods Game
• 2.8.1. Programming Challenge : Debugging
• 2.8.2. Summary
• 2.9.1. Mathematical Functions
• 2.9.2. Random Numbers
• 2.9.3. Programming Challenge : Random Numbers
• 2.9.4. Summary
• 2.10.1. Concept Summary
• 2.10.2. Java Keyword Summary
• 2.10.3. Vocabulary Practice
• 2.10.4. Common Mistakes
• 2.11. Mixed Up Code Practice
• 2.12. Toggle Mixed Up or Write Code Practice
• 2.13. Coding Practice
• 2.14. Practice Test for Objects (2.1-2.5)
• 2.15.1. Easier Multiple Choice Questions
• 2.15.2. Medium Multiple Choice Questions
• 2.15.3. Hard Multiple Choice Questions
• 2.16. Java Swing GUIs (optional)
• 3.1.1. Testing Equality (==)
• 3.1.2. Relational Operators (<, >)
• 3.1.3. Testing with remainder (%)
• 3.1.4. Programming Challenge : Prime Numbers POGIL
• 3.1.5. Summary
• 3.1.6. AP Practice
• 3.1.7. Relational Operators Practice Game
• 3.2.1. Relational Operators in If Statements
• 3.2.2. Common Errors with If Statements
• 3.2.3. Programming Challenge : Magic 8 Ball
• 3.2.4. Summary
• 3.2.5. AP Practice
• 3.3.1. Nested Ifs and Dangling Else
• 3.3.2. Programming Challenge : 20 Questions
• 3.3.3. Summary
• 3.3.4. AP Practice
• 3.4.1. Programming Challenge : Adventure
• 3.4.2. Summary
• 3.4.3. AP Practice
• 3.5.1. And (&&), Or (||), and Not (!)
• 3.5.2. Truth Tables
• 3.5.3. Short Circuit Evaluation
• 3.5.4. Programming Challenge : Truth Tables POGIL
• 3.5.5. Summary
• 3.5.6. AP Practice
• 3.5.7. Boolean Game
• 3.6.1. De Morgan’s Laws
• 3.6.2. Truth Tables
• 3.6.3. Simplifying Boolean Expressions
• 3.6.4. Programming Challenge : Truth Tables POGIL
• 3.6.5. Summary
• 3.6.6. AP Practice
• 3.7.1. String Equality
• 3.7.2. Equality with New Strings
• 3.7.3. Comparing with null
• 3.7.4. Programming Challenge : Tracing Code
• 3.7.5. Summary
• 3.7.6. AP Practice
• 3.8.1. Concept Summary
• 3.8.2. Java Keyword Summary
• 3.8.3. Vocabulary Practice
• 3.8.4. Common Mistakes
• 3.9. Mixed Up Code Practice
• 3.10. Toggle Mixed Up or Write Code Practice
• 3.11. Coding Practice
• 3.12.1. Easier Multiple Choice Questions
• 3.12.2. Medium Multiple Choice Questions
• 3.12.3. Hard Multiple Choice Questions
• 3.13.1. Magpie ChatBot Lab
• 3.13.2. Activity 2: Running Simplified Magpie Code
• 3.13.3. Activity 3: Better Keyword Detection
• 3.13.4. Activity 4: Responses that Transform Statements
• 3.13.5. Mixed Up Code Practice
• 3.14. More Coding Practice
• 4.1.1. Three Steps to Writing a Loop
• 4.1.2. Tracing Loops
• 4.1.3. Common Errors with Loops
• 4.1.4. Input-Controlled Loops
• 4.1.5. Programming Challenge : Guessing Game
• 4.1.6. Summary
• 4.1.7. AP Practice
• 4.2.1. Three Parts of a For Loop
• 4.2.2. Decrementing Loops
• 4.2.3. Turtle Loops
• 4.2.4. Programming Challenge : Turtles Drawing Shapes
• 4.2.5. Summary
• 4.2.6. AP Practice
• 4.3.1. While Find and Replace Loop
• 4.3.2. For Loops: Reverse String
• 4.3.3. Programming Challenge : String Replacement Cats and Dogs
• 4.3.4. Summary
• 4.4.1. Nested Loops with Turtles
• 4.4.2. Programming Challenge : Turtle Snowflakes
• 4.4.3. Summary
• 4.5.1. Tracing Loops
• 4.5.2. Counting Loop Iterations
• 4.5.3. Programming Challenge : POGIL Analyzing Loops
• 4.5.4. Summary
• 4.5.5. Loop Analysis Game
• 4.6.1. Concept Summary
• 4.6.2. Java Keyword Summary
• 4.6.3. Vocabulary Practice
• 4.6.4. Common Mistakes
• 4.7.1. Going Beyond Remainder 4
• 4.7.2. Look Deeper
• 4.7.3. More Practice
• 4.7.4. Long Division with a Remainder
• 4.7.5. Dividing Evenly
• 4.7.6. Describe the Remainder (%) Operator
• 4.8. Mixed Up Code Practice
• 4.9. Toggle Mixed Up or Write Code Practice
• 4.10. Coding Practice with Loops
• 4.11.1. Easier Multiple Choice Questions
• 4.11.2. Medium Multiple Choice Questions
• 4.11.3. More Practice
• 4.12.1. 2019 APCalendar FRQ
• 4.12.2. Part A: numberOfLeapYear()
• 4.12.3. How to solve numberOfLeapYears()
• 4.12.4. Part B: dayOfWeek()
• 4.13.1. How to solve this problem
• 4.13.2. Video - One way to code the solution
• 4.14.1. How to solve this problem
• 4.14.2. Figuring out the algorithm
• 4.14.3. Write the Code
• 4.14.4. Video - One way to code the solution
• 4.15.1. Activity 0 Analyzing Reviews
• 4.15.2. Activity 1 : Sentiment Value
• 4.15.3. Activity 2 :Total Sentiment Value and Star Ratings
• 4.15.4. Activity 3 : Autogenerate a Fake Review
• 4.15.5. Activity 4 : Create a More Positive or Negative Review
• 4.15.6. Activity 5 : Open-ended Activity
• 5.1.1. Creating a Class
• 5.1.2. Designing a Class
• 5.1.3. Instance Variables
• 5.1.4. Methods
• 5.1.5. Object-Oriented Design
• 5.1.6. Programming Challenge : Riddle Class
• 5.1.7. Design a Class for your Community
• 5.1.8. Summary
• 5.1.9. AP Practice
• 5.2.1. Constructor Signature
• 5.2.2. The Job of a Constructor
• 5.2.3. Advanced AP Topic: Reference parameters
• 5.2.4. Programming Challenge : Student Class
• 5.2.5. Design a Class for your Community
• 5.2.6. Summary
• 5.2.7. AP Practice
• 5.3.1. Comments
• 5.3.2. Preconditions and Postconditions
• 5.3.3. Software Validity and Use-Case Diagrams
• 5.3.4. Agile Software Development
• 5.3.5. Programming Challenge : Comments and Conditions
• 5.3.6. Summary
• 5.4.1. toString
• 5.4.2. Programming Challenge : Class Pet
• 5.4.3. Summary
• 5.4.4. AP Practice
• 5.5.1. How to write a setter
• 5.5.2. Programming Challenge : Class Pet Setters
• 5.5.3. Summary
• 5.5.4. AP Practice
• 5.6.1. Parameters
• 5.6.2. Programming Challenge : Song with Parameters
• 5.6.3. Design a Class for your Community
• 5.6.4. Summary
• 5.6.5. AP Practice
• 5.7.1. Programming Challenge : Static Song and counter
• 5.7.2. Summary
• 5.8.1. Programming Challenge : Debugging
• 5.8.2. Summary
• 5.8.3. AP Practice
• 5.9.1. Programming Challenge : Bank Account
• 5.9.2. Summary
• 5.9.3. AP Practice
• 5.10.1. POGIL Groupwork: Impacts of CS
• 5.10.2. Summary
• 5.11.1. Concept Summary
• 5.11.2. Java Keyword Summary
• 5.11.3. Vocabulary Practice
• 5.11.4. Common Mistakes
• 5.12. Mixed Up Code Practice
• 5.13. Toggle Mixed Up or Write Code Practice
• 5.14. Multiple-Choice Exercises
• 5.15. Midterm Test
• 5.16.1. 2019 StepTracker Class FRQ
• 5.16.2. Determining the Instance Variables
• 5.16.3. Writing the Class Header and Constructor
• 5.16.4. Writing the Accessor Method activeDays
• 5.16.5. Writing the Mutator Method addDailySteps
• 5.16.6. Writing the Accessor Method averageSteps
• 5.17. Free Response Question - Time
• 5.18.1. Try and Solve It
• 5.19. College Board Celebrity and Data Labs
• 5.20.1. Code your Class
• 5.20.2. Optional Swing GUI
• 6.1.1. Declaring and Creating an Array
• 6.1.2. Using new to Create Arrays
• 6.1.3. Initializer Lists to Create Arrays
• 6.1.4. Array length
• 6.1.5. Access and Modify Array Values
• 6.1.6. Programming Challenge : Countries Array
• 6.1.7. Design an Array of Objects for your Community
• 6.1.8. Summary
• 6.1.9. AP Practice
• 6.1.10. Arrays Game
• 6.2.1. Index Variables
• 6.2.2. For Loop to Traverse Arrays
• 6.2.3. Looping From Back to Front
• 6.2.4. Looping through Part of an Array
• 6.2.5. Common Errors When Looping Through an Array
• 6.2.6. Programming Challenge : SpellChecker
• 6.2.7. Design an Array of Objects for your Community
• 6.2.8. Summary
• 6.2.9. Arrays Game
• 6.3.1. Foreach Loop Limitations
• 6.3.2. Foreach Loop Algorithms
• 6.3.3. Programming Challenge : SpellChecker 2
• 6.3.4. Design an Array of Objects for your Community
• 6.3.5. Summary
• 6.4.1. Free Response - Horse Barn A
• 6.4.2. Free Response - Horse Barn B
• 6.4.3. Free Response - Self Divisor B
• 6.4.4. Free Response - Sound A
• 6.4.5. Free Response - Sound B
• 6.4.6. Free Response - Number Cube A
• 6.4.7. Free Response - Number Cube B
• 6.5.1. Concept Summary
• 6.5.2. Java Keyword Summary
• 6.5.3. Vocabulary Practice
• 6.5.4. Common Mistakes
• 6.6. Mixed Up Code Practice
• 6.7. Toggle Mixed Up or Write Code Practice
• 6.8.1. More Practice
• 6.9.1. Easier Multiple Choice Questions
• 6.9.2. Medium Multiple Choice Questions
• 6.9.3. Hard Multiple Choice Questions
• 6.10. Practice Exam for Arrays
• 6.11. More Code Practice with Arrays
• 7.1.1. Packages and imports
• 7.1.2. Declaring and Creating ArrayLists
• 7.1.3. Programming Challenge : FRQ Digits
• 7.1.4. Summary
• 7.2.1. size()
• 7.2.2. add(obj)
• 7.2.3. add(index,obj)
• 7.2.4. remove(index)
• 7.2.5. get(index) and set(index, obj)
• 7.2.6. Comparing arrays and ArrayList s
• 7.2.7. Programming Challenge : Array to ArrayList
• 7.2.8. Summary
• 7.3.1. Enhanced For Each Loop
• 7.3.2. For Loop
• 7.3.3. While Loop
• 7.3.4. ArrayList of Student Objects
• 7.3.5. Programming Challenge : FRQ Word Pairs
• 7.3.6. Summary
• 7.4.1. Free Response - String Scramble B
• 7.4.2. Free Response - Climbing Club A
• 7.4.3. Free Response - Climbing Club B
• 7.4.4. Free Response - Climbing Club C
• 7.4.5. Free Response - CookieOrder A
• 7.4.6. Free Response - CookieOrder B
• 7.4.7. Free Response - StringFormatter A
• 7.4.8. Free Response - StringFormatter B
• 7.4.9. Free Response - Delimiters A
• 7.4.10. Free Response - Delimiters B
• 7.4.11. Free Response - Grid World A
• 7.5.1. Sequential Search
• 7.5.2. Binary Search
• 7.5.3. Runtimes
• 7.5.4. Programming Challenge : Search Runtimes
• 7.5.5. Summary
• 7.6.1. Selection Sort
• 7.6.2. Insertion Sort
• 7.6.3. Programming Challenge : Sort Runtimes
• 7.6.4. Summary
• 7.7.1. POGIL Groupwork: Data Privacy
• 7.7.2. Summary
• 7.8.1. Concept Summary
• 7.8.2. Vocabulary Practice
• 7.8.3. Common Mistakes
• 7.9.1. Java File , Scanner , and IOException Classes
• 7.9.2. Reading in Data with Scanner
• 7.9.3. Reading in Files with java.nio.file
• 7.9.4. Object-Oriented Design with CSV Files
• 7.9.5. Programming Challenge: ArrayList of Objects from Input File
• 7.10. Mixed Up Code Practice
• 7.11. Toggle Mixed Up or Write Code Practice
• 7.12. Code Practice with ArrayLists
• 7.13.1. Easier Multiple Choice Questions
• 7.13.2. Medium Multiple Choice Questions
• 7.13.3. Hard Multiple Choice Questions
• 7.13.4. Easier Search/Sort Multiple Choice Questions
• 7.13.5. Medium Search/Sort Multiple Choice Questions
• 7.13.6. Hard Search/Sort Multiple Choice Questions
• 7.14. College Board Celebrity and Data Labs
• 8.1.1. 2D Arrays (Day 1)
• 8.1.2. Array Storage
• 8.1.3. How Java Stores 2D Arrays
• 8.1.4. Declaring 2D Arrays
• 8.1.5. Set Value(s) in a 2D Array (Day 2)
• 8.1.6. Initializer Lists for 2D Arrays
• 8.1.7. Get a Value from a 2D Array
• 8.1.8. Programming Challenge : ASCII Art
• 8.1.9. Summary
• 8.1.10. 2D Arrays Game
• 8.2.1. Nested Loops for 2D Arrays (Day 1)
• 8.2.2. Getting the Number of Rows and Columns
• 8.2.3. Looping Through a 2D Array
• 8.2.4. AP Practice
• 8.2.5. Enhanced For-Each Loop for 2D Arrays (Day 2)
• 8.2.6. 2D Array Algorithms
• 8.2.7. 2D Array of Objects
• 8.2.8. Programming Challenge : Picture Lab
• 8.2.9. Summary
• 8.2.10. AP Practice
• 8.2.11. 2D Arrays and Loops Game
• 8.3.1. Concept Summary
• 8.3.2. Vocabulary Practice
• 8.3.3. Common Mistakes
• 8.4. Mixed Up Code Practice
• 8.5. Toggle Mixed Up or Write Code Practice
• 8.6. Code Practice with 2D Arrays
• 8.7.1. Free Response - Gray Image A
• 8.7.2. Free Response - Gray Image B
• 8.7.3. Free Response - Route Cipher A
• 8.7.4. Free Response - Route Cipher B
• 8.8.1. Easier Multiple Choice Questions
• 8.8.2. Medium Multiple Choice Questions
• 8.8.3. Hard Multiple Choice Questions
• 8.9.1. Picture Lab A1 - A3
• 8.9.2. Picture Lab A4: 2D Arrays in Java
• 8.9.3. Picture Lab A5: Modifying a Picture
• 8.9.4. Picture Lab A6: Mirroring Pictures
• 8.9.5. Picture Lab A7: Mirroring Part of a Picture
• 8.9.6. Picture Lab A8: Creating a Collage
• 8.9.7. Picture Lab A9: Simple Edge Detection
• 8.10. More Code Practice with 2D Arrays
• 9.1.1. Inheritance (Day 1)
• 9.1.2. Subclass extends Superclass
• 9.1.3. Why Use Inheritance?
• 9.1.4. is-a vs. has-a (Day 2)
• 9.1.5. is-a Substitution Test
• 9.1.6. Programming Challenge : Online Store
• 9.1.7. Summary
• 9.2.1. Chain of initialization
• 9.2.2. Programming Challenge : Square is-a Rectangle
• 9.2.3. Summary
• 9.3.1. Overloading Methods
• 9.3.2. Inherited Get/Set Methods
• 9.3.3. Programming Challenge : Pet Sounds
• 9.3.4. Summary
• 9.4.1. Programming Challenge : Customer Info
• 9.4.2. Summary
• 9.5.1. Superclass References
• 9.5.2. Superclass Method Parameters
• 9.5.3. Superclass Arrays and ArrayLists
• 9.5.4. Programming Challenge : Shopping Cart
• 9.5.5. Summary
• 9.6.1. Programming Challenge : Shopping Cart 2
• 9.6.2. Summary
• 9.7.1. toString() method
• 9.7.2. equals Method
• 9.7.3. Overriding the equals Method
• 9.7.4. Programming Challenge : Savings Account
• 9.7.5. Summary
• 9.8.1. Concept Summary
• 9.8.2. Java Keyword Summary
• 9.8.3. Vocabulary Practice
• 9.8.4. Common Mistakes
• 9.9.1. Free Response - Trio A
• 9.9.2. Trio Student Solution 1
• 9.9.3. Trio Student Solution 2
• 9.9.4. Trio Student Solution 3
• 9.10. Mixed Up Code Practice
• 9.11. Toggle Mixed Up or Write Code Practice
• 9.12. Code Practice with Object Oriented Concepts
• 9.13.1. Easier Multiple Choice Questions
• 9.13.2. Medium Multiple Choice Questions
• 9.13.3. Hard Multiple Choice Questions
• 9.13.4. More Practice
• 9.14. College Board Celebrity Lab
• 10.1.1. What is Recursion? (Day 1)
• 10.1.2. Why use Recursion?
• 10.1.3. Factorial Method
• 10.1.4. Base Case
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• NCERT Solutions
• NCERT Class 9
• NCERT 9 Maths
• Chapter 6: Lines And Angles
• Exercise 6.1

NCERT Solutions for Class 9 Maths Chapter 6 - Lines And Angles Exercise 6.1

Most of the time, students don’t ask their doubts in class due to shyness. Due to this, they don’t get to know how the questions are being solved by the teacher. This happens most often in Maths class. In other subjects, students can still find the answer if they re-read the chapter. But for mathematics, if they miss the concepts, then they would not be able to solve them. So, to help students here, we have provided the detailed Exercise 6.1 NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles .

Students can download the NCERT Solutions of Class 9 Maths Chapter 6 Exercise 6.1 in PDF format by clicking on the link below. These solutions are prepared by subject experts and are described in detail. By going through NCERT Solutions PDF, students can easily understand the method of solving the questions.

NCERT Solutions for Class 9 Maths Chapter 6 – Lines And Angles Exercise 6.1

Access answers to ncert solutions for class 9 maths chapter 6 – lines and angles exercise 6.1.

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Access other Exercise Solutions of Class 9 Maths Chapter 6 – Lines and Angles

The NCERT Class 9 Chapter 6 Lines and Angles has two more exercises. Students can access the solutions of these exercises by visiting the link below.

Exercise 6.2 Solutions 6 Questions (3 Short Answer Questions, 3 Long Answer Question)

Exercise 6.3 Solutions 6 Questions (5 Short Answer Questions, 1 Long Answer Question)

NCERT Solutions for Class 9 Maths Chapter 6 – Lines and Angles Exercise 6.1

1. In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC +∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

From the diagram, we have

(∠AOC +∠BOE +∠COE) and (∠COE +∠BOD +∠BOE) forms a straight line.

So, ∠AOC+∠BOE +∠COE = ∠COE +∠BOD+∠BOE = 180°

Now, by putting the values of ∠AOC + ∠BOE = 70° and ∠BOD = 40° we get

∠COE = 110° and ∠BOE = 30°

So, reflex ∠COE = 360 o – 110 o = 250 o

2. In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.

We know that the sum of linear pair are always equal to 180°

∠POY +a +b = 180°

Putting the value of ∠POY = 90° (as given in the question) we get,

Now, it is given that a : b = 2 : 3 so,

Let a be 2x and b be 3x

∴ 2x+3x = 90°

Solving this we get

So, x = 18°

∴ a = 2×18° = 36°

Similarly, b can be calculated and the value will be

b = 3×18° = 54°

From the diagram, b+c also forms a straight angle so,

c+54° = 180°

3. In Fig. 6.15, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Since ST is a straight line so,

∠ PQS+ ∠ PQR = 180° (linear pair) and

∠ PRT+ ∠ PRQ = 180° (linear pair)

Now,  ∠ PQS +  ∠ PQR =  ∠ PRT+ ∠ PRQ = 180°

Since  ∠ PQR = ∠ PRQ (as given in the question)

∠ PQS =  ∠ PRT. (Hence proved).

4. In Fig. 6.16, if x+y = w+z, then prove that AOB is a line.

For proving AOB is a straight line, we will have to prove x+y is a linear pair

i.e. x+y = 180°

We know that the angles around a point are 360° so,

x+y+w+z = 360°

In the question, it is given that,

So, (x+y)+(x+y) = 360°

2(x+y) = 360°

∴ (x+y) = 180° (Hence proved).

5. In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = ½ (∠QOS – ∠POS).

In the question, it is given that (OR ⊥ PQ) and ∠POQ = 180°

We can write it as ∠ROP = ∠ROQ = 90 0

We know that

∠ROP = ∠ROQ

It can be written as

∠POS + ∠ROS = ∠ROQ

∠POS + ∠ROS = ∠QOS – ∠ROS

∠SOR + ∠ROS = ∠QOS – ∠POS

2∠ROS = ∠QOS – ∠POS

Or, ∠ROS = 1/2 (∠QOS – ∠POS)(Hence proved).

6. It is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

Here, XP is a straight line

So, ∠XYZ +∠ZYP = 180°

Putting the value of ∠XYZ = 64° we get,

64° +∠ZYP = 180°

∴ ∠ZYP = 116°

From the diagram, we also know that ∠ZYP = ∠ZYQ + ∠QYP

Now, as YQ bisects ∠ZYP,

∠ZYQ = ∠QYP

Or, ∠ZYP = 2∠ZYQ

∴ ∠ZYQ = ∠QYP = 58°

Again, ∠XYQ = ∠XYZ + ∠ZYQ

By putting the value of ∠XYZ = 64° and ∠ZYQ = 58° we get.

∠XYQ = 64°+58°

Or, ∠XYQ = 122°

Now, reflex ∠QYP = 180°+XYQ

We computed that the value of ∠XYQ = 122°.

∠QYP = 180°+122°

∴ ∠QYP = 302°

This exercise will help students recall the types of angles (acute, obtuse, right, straight, reflex, complementary and supplementary) that they have studied in earlier classes. The new concepts in the exercise will start from the intersecting and non-intersecting lines, and then Pairs of Angles are explained in detail along with a theorem proof, as well as some examples in the NCERT textbook.

The questions in the exercise are based on finding the value of angles from the given diagram and proving the statements. In the NCERT Class 9 Maths Solutions , we have provided step-by-step solutions along with the diagram for students’ convenience. Also, the questions are solved by the easiest method, so students can easily understand them.

We hope this information on “NCERT Solution for Class 9 Maths Chapter 6 Lines and Angles Exercise 6.1” is useful for students. Stay tuned for further updates on CBSE and other competitive exams. To access interactive Maths and Science Videos, download the BYJU’S App and subscribe to our YouTube Channel.

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