Class 9 Maths Chapter 6 Lines and Angles – Exercise 6.2 NCERT Solutions

Introduction

Exercise 6.2 explores the angle relationships formed when a transversal intersects parallel lines. You’ll practice identifying corresponding, alternate interior, and co‑interior angles, and use these properties to solve problems.

Key Concepts

• Corresponding Angles: Equal when lines are parallel.

• Alternate Interior Angles: Equal when lines are parallel.

• Co‑Interior Angles: Sum = 180° when lines are parallel.

• Transversal: A line that intersects two or more lines at distinct points.

Solved Questions (Step by Step)

Q1. If a transversal intersects two parallel lines, prove corresponding angles are equal.

Solution:

• By Euclid’s postulate, if a line intersects parallel lines, corresponding angles are equal.

Q2. If a transversal intersects two parallel lines, prove alternate interior angles are equal.

Solution:

• By Euclid’s postulate, alternate interior angles are equal.

Q3. If a transversal intersects two parallel lines, prove co‑interior angles are supplementary.

Solution:

• Sum of co‑interior angles = 180°.

Q4. If one angle is 70°, find its corresponding angle.

Solution:

• Corresponding angle = 70°.

Q5. If one angle is 120°, find its alternate interior angle.

Solution:

• Alternate interior angle = 120°.

Q6. If one angle is 65°, find its co‑interior angle.

Solution:

• Co‑interior angle = $180\mathrm{°}-65\mathrm{°}=115\mathrm{°}$.

Q7. If one angle is 85°, find its corresponding angle.

Solution:

• Corresponding angle = 85°.

Q8. If one angle is 95°, find its alternate interior angle.

Solution:

• Alternate interior angle = 95°.

Q9. If one angle is 110°, find its co‑interior angle.

Solution:

• Co‑interior angle = $180\mathrm{°}-110\mathrm{°}=70\mathrm{°}$.

Q10. If one angle is 50°, find its corresponding angle.

Solution:

• Corresponding angle = 50°.

Q11. If one angle is 130°, find its alternate interior angle.

Solution:

• Alternate interior angle = 130°.

Q12. If one angle is 40°, find its co‑interior angle.

Solution:

• Co‑interior angle = $180\mathrm{°}-40\mathrm{°}=140\mathrm{°}$.

Q13. If one angle is 75°, find its corresponding angle.

Solution:

• Corresponding angle = 75°.

Q14. If one angle is 105°, find its alternate interior angle.

Solution:

• Alternate interior angle = 105°.

Q15. If one angle is 60°, find its co‑interior angle.

Solution:

• Co‑interior angle = $180\mathrm{°}-60\mathrm{°}=120\mathrm{°}$.

FAQs (10 for Exercise 6.2)

1. Q: What is a transversal? A: A line that intersects two or more lines at distinct points.

2. Q: What are corresponding angles? A: Angles in matching corners when a transversal cuts parallel lines.

3. Q: What are alternate interior angles? A: Angles inside parallel lines but on opposite sides of the transversal.

4. Q: What are co‑interior angles? A: Angles inside parallel lines on the same side of the transversal.

5. Q: What is the sum of co‑interior angles? A: 180°.

6. Q: When are corresponding angles equal? A: When the lines are parallel.

7. Q: When are alternate interior angles equal? A: When the lines are parallel.

8. Q: What is the condition for parallel lines using angles? A: If corresponding or alternate interior angles are equal, lines are parallel.

9. Q: What is the condition for co‑interior angles? A: If co‑interior angles are supplementary, lines are parallel.

10. Q: Why are these properties important? A: They help prove lines are parallel and solve geometric problems.

Conclusion

Exercise 6.2 has 15 questions that strengthen your understanding of angle properties when a transversal intersects parallel lines. This builds the foundation for proving parallelism and solving geometric problems.

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