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

Introduction

Exercise 6.1 introduces the basic properties of angles formed by intersecting lines. You’ll learn about linear pairs, vertically opposite angles, and how to apply these properties to solve problems.

Key Concepts

• Linear Pair Axiom: If a ray stands on a line, the sum of adjacent angles is 180°.

• Vertically Opposite Angles: When two lines intersect, vertically opposite angles are equal.

• Supplementary Angles: Two angles whose sum is 180°.

Solved Questions (Step by Step)

Q1. If two angles form a linear pair and one angle is 70°, find the other.

Solution:

• Linear pair sum = 180°.

• Other angle = $180\mathrm{°}-70\mathrm{°}=110\mathrm{°}$.

Q2. If two angles form a linear pair and one angle is 125°, find the other.

Solution:

• Other angle = $180\mathrm{°}-125\mathrm{°}=55\mathrm{°}$.

Q3. If two lines intersect and one angle is 75°, find its vertically opposite angle.

Solution:

• Vertically opposite angles are equal.

• Angle = 75°.

Q4. If two lines intersect and one angle is 120°, find its vertically opposite angle.

Solution:

• Angle = 120°.

Q5. If two lines intersect and one angle is 45°, find its adjacent angle.

Solution:

• Adjacent angle = $180\mathrm{°}-45\mathrm{°}=135\mathrm{°}$.

Q6. If two lines intersect and one angle is 90°, find all other angles.

Solution:

• Vertically opposite = 90°.

• Adjacent = $180\mathrm{°}-90\mathrm{°}=90\mathrm{°}$.

• All angles = 90°.

Q7. If two lines intersect and one angle is 30°, find all other angles.

Solution:

• Vertically opposite = 30°.

• Adjacent = $180\mathrm{°}-30\mathrm{°}=150\mathrm{°}$.

• Other vertically opposite = 150°.

Q8. If two lines intersect and one angle is 135°, find all other angles.

Solution:

• Vertically opposite = 135°.

• Adjacent = $180\mathrm{°}-135\mathrm{°}=45\mathrm{°}$.

• Other vertically opposite = 45°.

Q9. If two lines intersect and one angle is 60°, find its adjacent angle.

Solution:

• Adjacent = $180\mathrm{°}-60\mathrm{°}=120\mathrm{°}$.

Q10. If two lines intersect and one angle is 150°, find its adjacent angle.

Solution:

• Adjacent = $180\mathrm{°}-150\mathrm{°}=30\mathrm{°}$.

Q11. If two lines intersect and one angle is 40°, find all other angles.

Solution:

• Vertically opposite = 40°.

• Adjacent = $180\mathrm{°}-40\mathrm{°}=140\mathrm{°}$.

• Other vertically opposite = 140°.

Q12. If two lines intersect and one angle is 20°, find all other angles.

Solution:

• Vertically opposite = 20°.

• Adjacent = $180\mathrm{°}-20\mathrm{°}=160\mathrm{°}$.

• Other vertically opposite = 160°.

Q13. If two lines intersect and one angle is 85°, find its adjacent angle.

Solution:

• Adjacent = $180\mathrm{°}-85\mathrm{°}=95\mathrm{°}$.

Q14. If two lines intersect and one angle is 100°, find its vertically opposite angle.

Solution:

• Vertically opposite = 100°.

Q15. If two lines intersect and one angle is 50°, find all other angles.

Solution:

• Vertically opposite = 50°.

• Adjacent = $180\mathrm{°}-50\mathrm{°}=130\mathrm{°}$.

• Other vertically opposite = 130°.

FAQs (10 for Exercise 6.1)

1. Q: What is a linear pair of angles? A: Two adjacent angles whose sum is 180°.

2. Q: What are vertically opposite angles? A: Angles opposite each other when two lines intersect.

3. Q: Are vertically opposite angles always equal? A: Yes, by Euclid’s axioms.

4. Q: What is the sum of angles in a linear pair? A: 180°.

5. Q: Can two acute angles form a linear pair? A: No, because their sum is less than 180°.

6. Q: Can two obtuse angles form a linear pair? A: No, because their sum is more than 180°.

7. Q: Can one acute and one obtuse angle form a linear pair? A: Yes, if their sum is 180°.

8. Q: What is the difference between adjacent and vertically opposite angles? A: Adjacent share a common arm; vertically opposite do not.

9. Q: What is the sum of all angles around a point? A: 360°.

10. Q: Why are these properties important? A: They form the basis for solving geometric problems involving lines and angles.

Conclusion

Exercise 6.1 has 15 questions that strengthen your understanding of linear pairs and vertically opposite angles. This builds the foundation for more complex angle properties in triangles and polygons.

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