Class 9 Maths Chapter 6 Lines and Angles NCERT Solutions: All Exercises Step-by-Step Solved

Introduction

Lines and angles form the backbone of geometry in Class 9 CBSE Maths Chapter 6. You learn types of angles, parallel lines with transversals, and triangle properties like angle sum 180 degrees.

Key ideas include vertically opposite angles equal, linear pairs sum to 180, and theorems on alternate/corresponding angles. Three exercises build from basics to proofs.

Key Formulas and Properties

• Vertically opposite angles equal.

• Linear pair: adjacent angles sum to 180 deg.

• Parallel lines + transversal: alternate interior equal, corresponding equal, co-interior sum 180 deg.

• Triangle angle sum: 180 deg.

• Exterior angle = sum interior opposite angles.

Exercise 6.1 Solved Questions

Q1: In figure, find x + y if lines intersect.

Solution: Vertically opposite: x = 62 deg, y = 58 deg. x + y = 120 deg.

Q2: Adjacent angles on straight line sum 180: find angle.

Solution: 115 + angle = 180, angle = 65 deg.

Q3: Linear pair: two adjacent sum 180.

Solution: Yes, by definition.

Q4: In Fig 6.13, AB CD intersect O. angle AOC + BOE =70, BOD=40. Find BOE, reflex COE.

Solution: Vert opp: angle AOC = BOD =40 deg. So BOE =70-40=30 deg. angle COE = 180 -30 =150, reflex 360-150=210 deg.

Q5: Adjacent not linear pair? Yes if not straight line.

Exercise 6.2 Solved Questions

Q1: Form pairs corresponding angles when parallel + transversal.

Solution: Identify pairs like top-left, bottom-right etc.

Q2: In Fig, AB||CD, transversal. If pair alternate interior equal, prove parallel. Use converse theorem.

Solution: Alternate interior equal implies parallel.

Q3: Lines AB CD intersect O. angle AOC + BOE=70, BOD=40 find BOE.

Solution: Same as 6.1 Q4: BOE=30 deg.

Q4: AB||CD||EF, y:z=3:7 find x.

Solution: Co-interior y + z =180. y=45, z=105? Wait y/z=3/7, y+ z=180. 10 parts=180, part=18, y=54, z=126. x=corresponding to y=54 deg.

Q5: Prove if corresponding equal, lines parallel.

Solution: By corresponding angles postulate converse.

Q6: In parallelogram, consecutive angles supplementary.

Solution: Opposite sides parallel, co-interior 180.

Exercise 6.3 Solved Questions

Q1: Triangle angle sum 180 deg.

Solution: Draw parallel to base through vertex, alternate angles equal, linear pair.

Q2: Two angles triangle given, find third.

Solution: 180 - sum.

Q3: Exterior angle = interior opp sum.

Solution: Extend side, exterior + adjacent interior =180, adjacent = other two interiors sum.

Q4: Angles 50,60 find third: 70 deg.

Q5: Prove exterior = sum opp interiors.

Solution: Linear pair exterior + one interior=180, that interior + other two=180, so equal.

15 FAQs

1. Vertically opposite angles? Equal.

2. Linear pair sum? 180 deg.

3. Alternate interior? Equal if parallel.

4. Corresponding angles? Equal if parallel.

5. Co-interior sum? 180 deg.

6. Triangle angles sum? 180 deg.

7. Exterior angle triangle? Sum opp interiors.

8. Parallel lines never? Intersect.

9. Transversal crosses? Two lines.

10. Reflex angle? >180 <360.

11. Complementary? Sum 90.

12. Supplementary? Sum 180.

13. Adjacent angles? Common arm/vertex.

14. Angle sum proof? Parallel to base.

15. Converse theorem? Angles imply parallel.

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