LINES & ANGLES

UNLOCKING GEOMETRY

Introduction

In Geometry, lines and angles are the foundation of all shapes and structures. Understanding them helps in solving real-life problems like construction, design, and measurements.

Key Concepts and Definitions

Lines

• Line: Extends infinitely in both directions
• Line Segment: Has two endpoints
• Ray: Starts at one point and extends infinitely in one direction

Angles

An angle is formed by two rays with a common endpoint (vertex).

Types of Angles

• Acute Angle: < 90°
• Right Angle: = 90°
• Obtuse Angle: Between 90° and 180°
• Straight Angle: = 180°
• Reflex Angle: > 180°

Theorems and Properties

Pairs of Angles

• Complementary → Sum = 90°
• Supplementary → Sum = 180°
• Adjacent Angles → Share a side
• Linear Pair → Sum = 180°

Angle Relationships

• Vertically Opposite Angles → Equal

Transversal & Parallel Lines

• Corresponding Angles → Equal
• Alternate Interior Angles → Equal
• Alternate Exterior Angles → Equal
• Consecutive Interior Angles → Sum = 180°

Examples

• 35° → Acute Angle
• Complement of 25° → 65°
• Linear pair with 120° → 60°
• Vertically opposite angles → Equal

📝 Practice MCQs (50 Questions)

Basic Concepts (1–10)

1. A line extends in:
   A) One direction
   B) Two directions infinitely
   C) Fixed length
   D) Circular path
2. A ray has:
   A) No endpoints
   B) One endpoint
   C) Two endpoints
   D) Infinite endpoints
3. A line segment has:
   A) One endpoint
   B) No endpoint
   C) Two endpoints
   D) Infinite endpoints
4. Angle is formed by:
   A) Two lines
   B) Two rays
   C) Two points
   D) Two segments
5. Vertex is:
   A) Starting point of ray
   B) Meeting point of two rays
   C) Middle point
   D) End of line
6. Which is acute angle?
   A) 100°
   B) 90°
   C) 45°
   D) 180°
7. Right angle measure:
   A) 45°
   B) 90°
   C) 180°
   D) 60°
8. Straight angle is:
   A) 90°
   B) 180°
   C) 360°
   D) 45°
9. Reflex angle is:
   A) < 90°
   B) = 90°
   C) > 180°
   D) = 180°
10. Obtuse angle lies between:
    A) 0°–90°
    B) 90°–180°
    C) 180°–360°
    D) 0°–180°

Angle Relationships (11–20)

11. Complementary angles sum:
    A) 180°
    B) 360°
    C) 90°
    D) 45°
12. Supplementary angles sum:
    A) 90°
    B) 180°
    C) 360°
    D) 60°
13. Adjacent angles share:
    A) Vertex only
    B) Side only
    C) Vertex and side
    D) Nothing
14. Linear pair sum:
    A) 90°
    B) 180°
    C) 360°
    D) 45°
15. Vertically opposite angles are:
    A) Unequal
    B) Equal
    C) Supplementary
    D) Complementary
16. Complement of 30°:
    A) 60°
    B) 90°
    C) 120°
    D) 30°
17. Supplement of 70°:
    A) 110°
    B) 100°
    C) 90°
    D) 80°
18. Two right angles are:
    A) Complementary
    B) Supplementary
    C) Adjacent
    D) None
19. Two angles sum 90° →
    A) Supplementary
    B) Complementary
    C) Linear pair
    D) Adjacent
20. Linear pair are:
    A) Equal
    B) Adjacent & sum 180°
    C) 90°
    D) None

Transversal & Parallel Lines (21–35)

21. A transversal:
    A) Parallel line
    B) Intersects two lines
    C) Curve
    D) Ray
22. Corresponding angles are:
    A) Unequal
    B) Equal
    C) 90°
    D) 180°
23. Alternate interior angles are:
    A) Equal
    B) Unequal
    C) 90°
    D) 60°
24. Alternate exterior angles are:
    A) Equal
    B) Unequal
    C) 45°
    D) 30°
25. Consecutive interior angles sum:
    A) 90°
    B) 180°
    C) 360°
    D) 60°
26. If corresponding angles equal → lines are:
    A) Intersecting
    B) Parallel
    C) Same
    D) Perpendicular
27. If alternate interior angles equal → lines are:
    A) Parallel
    B) Perpendicular
    C) Intersecting
    D) Curved
28. If sum is 180° → lines are:
    A) Parallel
    B) Not parallel
    C) Same
    D) Straight
29. Parallel lines never:
    A) Meet
    B) Extend
    C) Exist
    D) Intersect
30. Vertical angles occur when:
    A) Lines intersect
    B) Lines parallel
    C) Lines curve
    D) Lines stop
31. Vertical angles are:
    A) Equal
    B) Unequal
    C) 90°
    D) 180°
32. Transversal cuts lines at:
    A) Same point
    B) Different points
    C) No point
    D) Infinite
33. Alternate angles are:
    A) Same side
    B) Opposite side
    C) Same line
    D) None
34. Exterior angles lie:
    A) Inside
    B) Outside
    C) Middle
    D) Vertex
35. Interior angles lie:
    A) Outside
    B) Inside
    C) Edge
    D) Curve

Application-Based (36–50)

36. Complement of 52°:
    A) 38°
    B) 48°
    C) 58°
    D) 28°
37. Supplement of 120°:
    A) 60°
    B) 50°
    C) 70°
    D) 80°
38. Linear pair angle of 150°:
    A) 30°
    B) 40°
    C) 50°
    D) 60°
39. Vertically opposite of 80°:
    A) 80°
    B) 100°
    C) 90°
    D) 70°
40. If one angle is 110°, its adjacent linear pair:
    A) 70°
    B) 60°
    C) 50°
    D) 80°
41. If alternate interior = 60°, other is:
    A) 60°
    B) 120°
    C) 90°
    D) 30°
42. If corresponding angle = 75°, other is:
    A) 75°
    B) 105°
    C) 90°
    D) 60°
43. If interior angles sum 180°, lines are:
    A) Parallel
    B) Perpendicular
    C) Intersecting
    D) Curve
44. Angle >180° is:
    A) Acute
    B) Reflex
    C) Right
    D) Straight
45. Angle =180° is:
    A) Reflex
    B) Straight
    C) Acute
    D) Right
46. Angle <90° is:
    A) Acute
    B) Obtuse
    C) Reflex
    D) Straight
47. Angle between 90°–180°:
    A) Acute
    B) Obtuse
    C) Reflex
    D) Straight
48. A full angle is:
    A) 180°
    B) 360°
    C) 90°
    D) 270°
49. Two angles equal and opposite →
    A) Vertical
    B) Adjacent
    C) Linear
    D) Complementary
50. If one angle = 45°, complement is:
    A) 45°
    B) 90°
    C) 135°
    D) 60°

✅ Answer Key

1-B, 2-B, 3-C, 4-B, 5-B
6-C, 7-B, 8-B, 9-C, 10-B
11-C, 12-B, 13-C, 14-B, 15-B
16-A, 17-A, 18-B, 19-B, 20-B
21-B, 22-B, 23-A, 24-A, 25-B
26-B, 27-A, 28-A, 29-A, 30-A
31-A, 32-B, 33-B, 34-B, 35-B
36-A, 37-A, 38-A, 39-A, 40-A
41-A, 42-A, 43-A, 44-B, 45-B
46-A, 47-B, 48-B, 49-A, 50-A