Class 7 Maths Chapter 5 | Lines and Angles Full Chapter Explanation & NCERT Solutions

Introduction

This tutorial provides a comprehensive explanation of Class 7 Maths Chapter 5, focusing on Lines and Angles. We'll break down key concepts such as complementary angles, supplementary angles, linear pairs, and more, along with NCERT solutions to exercises. This guide aims to enhance your understanding of the topic and prepare you for exams.

Step 1: Understanding Complementary Angles

• Definition: Two angles are complementary if their sum is 90 degrees.
• Practical Tip: To find a complementary angle, subtract the given angle from 90 degrees.
  • Example: If the angle is 30 degrees, the complementary angle is 90 - 30 = 60 degrees.

Step 2: Exploring Supplementary Angles

• Definition: Two angles are supplementary if their sum is 180 degrees.
• Practical Tip: Use the same subtraction method to find a supplementary angle.
  • Example: For an angle of 110 degrees, the supplementary angle is 180 - 110 = 70 degrees.

Step 3: Adjacent Angles

• Definition: Adjacent angles are two angles that share a common side and a vertex.
• Visual Aid: Draw two angles that meet at a point to illustrate adjacency.

Step 4: Learning About Linear Pairs

• Definition: A linear pair consists of two adjacent angles whose non-common sides form a straight line.
• Key Point: The sum of angles in a linear pair is always 180 degrees.

Step 5: Vertically Opposite Angles

• Definition: When two lines intersect, the angles that are opposite each other are called vertically opposite angles.
• Key Property: Vertically opposite angles are equal.

Step 6: Pairs of Lines

• Types of Lines:
  • Parallel Lines: Lines that never meet and are always the same distance apart.
  • Intersecting Lines: Lines that cross each other at a point.
• Practical Application: Understand how these concepts apply to real-world scenarios like construction and engineering.

Step 7: Angles Made by a Transversal

• Definition: A transversal is a line that crosses two or more other lines.
• Key Concepts:
  • Corresponding Angles: Angles that occupy the same relative position at each intersection.
  • Alternate Interior Angles: Angles on opposite sides of the transversal, inside the two lines.

Step 8: Solving Exercise 5.1

• Questions 1 to 7: Work through these problems focusing on identifying angle types and relationships.
• Questions 8 to 10: Focus on applying the concepts learned about complementary and supplementary angles.

Step 9: Solving Exercise 5.2

• Questions 1 to 3: Continue practicing with more complex problems that integrate previously learned concepts.
• Questions 4 to 6: Ensure you can apply the definitions and properties of angles and lines correctly.

Conclusion

This tutorial covered the essential concepts of Lines and Angles, including definitions, properties, and practical examples. Understanding these concepts is crucial for solving related problems in your exercises. To reinforce your learning, practice the exercise questions provided and revisit any sections that need further clarification. For more resources, consider exploring the full course on the Magnet Brains website.