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**Lines and Angles Class 9 Worksheet with Solutions:** Worksheets focusing on lines and angles provide an ideal platform for students to familiarize themselves with a variety of angle-related problems and scenarios, aligning with the **CBSE syllabus**. These resources serve as valuable tools for students aiming to enhance their proficiency in angle concepts as outlined in **NCERT solutions** and **NCERT exemplar solutions**. Covering topics such as angle nomenclature, line identification, angle classification, angle measurement, and other engaging concepts, lines and angles worksheets offer a comprehensive approach to learning and practicing angles in accordance with the CBSE curriculum.

**NCERT Solutions for Class 9 All Subjects**

**NCERT Solutions for Class 9 Maths****NCERT Solutions for Class 9 Science****NCERT Solutions for Class 9 Social Science****NCERT Solutions for Class 9 English**

## Mastering CBSE Worksheet Class 9 Maths Chapter 6: Lines and Angles

In Class 9 Mathematics, understanding lines and angles is important. Chapter 6 of CBSE’s curriculum delves deep into this fundamental concept, laying the groundwork for more advanced mathematical principles. Let’s unravel the intricacies of Lines and Angles Class 9 Worksheet with Solutions in this comprehensive guide.

**You can also access free Exemplar Solutions**

**NCERT Exemplar Solutions Class 9 Maths Chapter 1****NCERT Exemplar Solutions Class 9 Maths Chapter 2****NCERT Notes – Class 9 Maths Chapter 2 Polynomials****NCERT Exemplar Solutions Class 9 Maths Chapter 5****Euclid’s Geometry Class 9 Notes Maths Chapter 5****NCERT Exemplar Solutions Class 9 Maths Chapter 6****NCERT Exemplar Solutions Class 9 Maths Chapter 7****Triangles Class 9 Notes Maths Chapter 7**

## Introduction to Lines and Angles

Lines and angles form the backbone of geometric reasoning. A line is a straight path that extends infinitely in both directions, while an angle is formed when two lines meet at a common point. These basic definitions set the stage for exploring their properties and relationships.

### Types of Lines

**a. Straight Lines**

Straight lines are those that do not bend or curve. They have a constant direction and extend indefinitely in both directions.

**b. Parallel Lines**

Parallel lines are lines that never intersect, no matter how far they extended. They maintain the same distance throughout their length.

**c. Perpendicular Lines**

Perpendicular lines intersect at a right angle, forming four right angles at the point of intersection.

### Types of Angles

**a. Acute Angle**

An acute angle is less than 90 degrees, making it sharper than a right angle.

**b. Right Angle**

A right angle is a precise 90-degree measurement, forming an immaculate L-shape.

**c. Obtuse Angle**

Beyond the right angle’s confines lies the obtuse angle, spanning over 90 degrees but stopping short of 180. It offers a broader perspective while maintaining a sense of restraint.

**Also Refer**: **NCERT Solutions Class 9 Chapter 6 Lines and Angles**

### Properties of Lines and Angles

Understanding the properties of lines and angles is crucial for solving geometric problems efficiently. Some key properties include:

- The total measure of angles formed around a point equals 360 degrees.
- When lines form a straight path, the sum of their angles is 180 degrees.
- Angles positioned across from one another, known as vertically opposite angles, share equal measures.
- If a transversal intersects two parallel lines, corresponding angles are congruent.

**CBSE Worksheets Class 9 for All Subjects**

**CBSE Worksheets for Class 9 Maths****CBSE Worksheets for Class 9 Science****CBSE Worksheets for Class 9 English****CBSE Worksheets for Class 9 Biology****CBSE Worksheets for Class 9 Chemistry****CBSE Worksheets for Class 9 Physics**

### Benefits of Solving Lines and Angles Class 9 Worksheet

Here are some benefits of solving Lines and Angles worksheet of Class 9:

**Understanding Geometry Concepts: CBSE Worksheets** help students grasp fundamental concepts related to lines and angles, such as types of angles (acute, obtuse, right), properties of parallel lines, and angle relationships (vertical angles, corresponding angles, alternate interior angles).

**Critical Thinking:** Many worksheets include challenging problems that require critical thinking and problem-solving skills. Students must apply their knowledge to analyze geometric relationships and devise strategies to solve problems effectively.

**Visual Representation:** Worksheets often include diagrams and visual representations of geometric figures, which help students visualize abstract concepts and make connections between mathematical ideas and real-world scenarios.

**Skill Development:** By working through lines and angles worksheets, students develop essential mathematical skills, such as spatial reasoning, logical thinking, and precision in mathematical reasoning.

**Self-Assessment:** Worksheets offer opportunities for self-assessment, as students can check their answers and identify areas where they may need additional practice or support.

**Preparation for Assessments:** Working on worksheets prepares students for assessments, including quizzes, tests, and standardized exams, by familiarizing them with the types of problems they may encounter and the strategies needed to solve them.

## Sample Worksheet: Lines and Angles Class 9 Worksheet with Solutions

Now equipped with the knowledge of lines and angles, let’s tackle CBSE worksheets with confidence. Practice identifying different types of angles and lines, and apply the properties learned to solve problems effectively.

Name: _______________________ Class: 9 Date: _______________

**Instructions:**

- Attempt all questions.
- Show all necessary steps in your solutions.
- Use a protractor where required.
- Write the answer in the given space.

**Questions 1:**

In the given figure, if ∠1 = 4x + 12 and ∠2 = 3x + 20, find the value of x and the measure of each angle.

Solution:

Value of x = _______

Measure of ∠1 = _______ degrees

Measure of ∠2 = _______ degrees

**Questions 2:**

In the given figure, ∠ABC = 3y + 15 and ∠CBD = 4y – 5. Find the value of y and the measure of each angle.

Solution:

Value of y = _______

Measure of ∠ABC = _______ degrees

Measure of ∠CBD = _______ degrees

**Questions 3:**

If ∠1 and ∠2 are complementary angles and m(∠1) = 4x + 10 and m(∠2) = 5x – 20, find the measure of each angle.

Solution:

Measure of ∠1 = _______ degrees

Measure of ∠2 = _______ degrees

**Questions 4:**

In the given figure, if ∠1 = 3x – 5 and ∠2 = 2x + 10, find the value of x and the measure of each angle.

Solution:

Value of x = _______

Measure of ∠1 = _______ degrees

Measure of ∠2 = _______ degrees

**Questions 5:**

In the given figure, if ∠1 = 2x + 30 and ∠2 = 3x – 10, find the value of x and the measure of each angle.

Solution:

Value of x = _______

Measure of ∠1 = _______ degrees

Measure of ∠2 = _______ degrees

**Questions 6:**

In the given figure, if ∠1 = 2x – 10 and ∠2 = 3x + 20, find the value of x and the measure of each angle.

Solution:

Value of x = _______

Measure of ∠1 = _______ degrees

Measure of ∠2 = _______ degrees

**Questions 7:**

If two adjacent angles are supplementary and one angle measures 4x – 10 and the other measures 3x + 20, find the measure of each angle.

Solution:

Measure of one angle = _______ degrees

Measure of the other angle = _______ degrees

**Questions 8:**

In the given figure, if m∠PQR = 2x + 10 and m∠QRS = 3x – 5, find the value of x and the measure of each angle.

Solution:

Value of x = _______

Measure of ∠PQR = _______ degrees

Measure of ∠QRS = _______ degrees

**Questions 9:**

If two angles are complementary and one angle measures 5x – 10 and the other measures 3x + 30, find the value of x and the measure of each angle.

Solution:

Value of x = _______

Measure of one angle = _______ degrees

Measure of the other angle = _______ degrees

**Questions 10:**

In the given figure, if ∠1 and ∠2 form a linear pair and ∠1 = 4x – 10 and ∠2 = 3x + 20, find the value of x and the measure of each angle.

Solution:

Value of x = _______

Measure of ∠1 = _______ degrees

Measure of ∠2 = _______ degrees

**Answer Key:**

**Answers 1:**

Value of x = 148/7

Measure of ∠1 = 64°

Measure of ∠2 = 116°

**Answers 2:**

Value of y = 40

Measure of ∠ABC = 135°

Measure of ∠CBD = 125°

**Answers 3:**

Measure of ∠1 = 30°

Measure of ∠2 = 60°

**Answers 4:**

Value of x = 15

Measure of ∠1 = 40°

Measure of ∠2 = 70°

**Answers 5:**

Value of x = 20

Measure of ∠1 = 70°

Measure of ∠2 = 80°

**Answers 6:**

Value of x = 15

Measure of ∠1 = 20°

Measure of ∠2 = 65°

**Answers 7:**

Measure of one angle = 50°

Measure of the other angle = 40°

**Answers 8:**

Value of x = 15

Measure of ∠PQR = 40°

Measure of ∠QRS = 35°

**Answers 9:**

Value of x = 8

Measure of one angle = 30°

Measure of the other angle = 60°

**Answers 10:**

Value of x = 15

Measure of ∠1 = 50°

Measure of ∠2 = 65°

### Conclusion

Mastering Chapter 6 of Class 9 Maths, “Lines and Angles,” is essential for building a strong foundation in geometry. By understanding the types of lines, angles, and their properties, students can excel in solving mathematical problems with ease. Continuous practice and application of concepts through CBSE worksheets will reinforce learning and ensure success in examinations.