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About Lines & Angles — Class 6 CBSE

Explore points, rays, line segments, and measure and classify different types of angles. This topic is part of the CBSE Class 6 mathematics syllabus (chapter: Chapter 2). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Lines & Angles

  • Introduction to Basic Geometric Ideas: Points, Lines, Rays, and Line Segments
  • Understanding Angles: Definition, Vertex, and Arms
  • Measuring and Classifying Angles: Acute, Right, Obtuse, and Straight
  • Special Cases: Reflex, Zero, and Complete Angles
  • Summary, Connections, and Practice for Lines & Angles

Interactive lesson · about 15 minutes · checkpoint question after every unit

Lines & Angles — solved examples for Class 6 CBSE

Example 1easy

Which of the following best describes a point in geometry?
  1. A)A figure with length and width
  2. B)A specific location that has no dimension
  3. C)A path extending infinitely in one direction
  4. D)A straight path with two endpoints

Step-by-step solution

  1. A point is a fundamental concept in geometry. It represents an exact position or location in space.
  2. By definition, a point has no dimension; it has no length, width, or depth. It is often represented by a dot.

Answer: A specific location that has no dimension

Example 2medium

Which of the following statements correctly defines a 'line segment'?
  1. A)A part of a line with two definite endpoints.
  2. B)A straight path that extends endlessly in one direction.
  3. C)A straight path that extends endlessly in both directions.
  4. D)A specific location or position in space.

Step-by-step solution

  1. A point is a specific location.
  2. A line extends endlessly in both directions.
  3. A ray extends endlessly in one direction from a starting point.
  4. A line segment is a part of a line that has two distinct endpoints, meaning it has a definite length.

Answer: A part of a line with two definite endpoints.

Example 3hard

Imagine 5 distinct points on a plane. If 3 of these points are collinear, and no other 3 points are collinear, how many unique straight lines can be drawn by joining any two of these points?
  1. A)8
  2. B)9
  3. C)10
  4. D)11

Step-by-step solution

  1. First, calculate the number of lines if all 5 points were non-collinear. This is given by the combination formula n(n-1)/2.
    5×(51)/2=5×4/2=10uniquelines.5 × (5-1) / 2 = 5 × 4 / 2 = 10 unique lines.
  2. Next, consider the 3 collinear points. If they were non-collinear, they would form 3 × (3-1) / 2 = 3 lines. However, since they are collinear, they form only 1 line.
  3. So, we subtract the lines 'lost' due to collinearity (3 lines) and add back the single line they actually form.
    Totallines=10(from5points)3(lineslostfrom3collinearpoints)+1(thesinglelineformedbythe3collinearpoints)=8lines.Total lines = 10 (from 5 points) - 3 (lines lost from 3 collinear points) + 1 (the single line formed by the 3 collinear points) = 8 lines.

Answer: 8

Practice questions on Lines & Angles

  1. Q1.easy

    What is the key characteristic that distinguishes a line segment from a line?
    1. A)It has only one endpoint
    2. B)It has no endpoints
    3. C)It has two distinct endpoints
    4. D)It extends infinitely in both directions
    Show answer

    Answer: It has two distinct endpoints

    Hint: Consider how you would measure a line segment compared to an entire line.

  2. Q2.easy

    Which statement accurately defines a ray?
    1. A)It has two endpoints and a definite length.
    2. B)It extends infinitely in both directions with no endpoints.
    3. C)It is a specific location with no dimension.
    4. D)It has one endpoint and extends infinitely in one direction.
    Show answer

    Answer: It has one endpoint and extends infinitely in one direction.

    Hint: Imagine a beam of light originating from a source – it has a start but no end.

  3. Q3.easy

    Imagine a perfectly straight railway track that seems to go on forever in both directions. Which geometric term best describes this track?
    1. A)Point
    2. B)Line segment
    3. C)Ray
    4. D)Line
    Show answer

    Answer: Line

    Hint: Focus on the phrase 'goes on forever in both directions'.

  4. Q4.medium

    A carpenter is building a wooden frame. He joins two pieces of wood at a corner to form an angle that looks exactly like the corner of a square tile. What type of angle has he formed?
    1. A)Acute angle
    2. B)Right angle
    3. C)Obtuse angle
    4. D)Straight angle
    Show answer

    Answer: Right angle

    Hint: Think about the angle formed at the corner of a square or a book. What is its measure?

  5. Q5.medium

    If an angle measures 75°, which of the following statements is true about it?
    1. A)It is an obtuse angle.
    2. B)It is a right angle.
    3. C)It is an acute angle.
    4. D)It is a straight angle.
    Show answer

    Answer: It is an acute angle.

    Hint: Remember the definitions of different types of angles based on their measure relative to 90° and 180°.

  6. Q6.medium

    Two lines are drawn on a paper such that they never intersect, no matter how far they are extended. What type of lines are these?
    1. A)Intersecting lines
    2. B)Perpendicular lines
    3. C)Concurrent lines
    4. D)Parallel lines
    Show answer

    Answer: Parallel lines

    Hint: Consider the definition of lines that maintain a constant distance from each other and never meet.

  7. Q7.hard

    Line P is perpendicular to Line Q. Line Q is parallel to Line R. Which of the following statements must be true?
    1. A)Line P is parallel to Line R.
    2. B)Line P is perpendicular to Line R.
    3. C)Line P intersects Line R but not necessarily perpendicularly.
    4. D)Line R is perpendicular to Line Q.
    Show answer

    Answer: Line P is perpendicular to Line R.

    Hint: Visualize the lines. If Line P makes a right angle with Line Q, and Line Q runs in the same direction as Line R, what angle will Line P make with Line R?

  8. Q8.hard

    A clock shows the time as 3:00. What is the measure of the reflex angle formed by the hour hand and the minute hand?
    1. A)90°
    2. B)180°
    3. C)270°
    4. D)300°
    Show answer

    Answer: 270°

    Hint: First, determine the smaller angle between the hands at 3:00. Then, remember that a reflex angle is the larger angle, which is greater than 180° but less than 360°.

  9. Q9.hard

    Rohan observes an angle measuring 181° and classifies it as an obtuse angle. His friend, Priya, says it's a straight angle. Who is correct, and why?
    1. A)Rohan is correct, as 181° is greater than 90°.
    2. B)Priya is correct, as it is close to 180°.
    3. C)Neither is correct; it is a reflex angle.
    4. D)Neither is correct; it is a complete angle.
    Show answer

    Answer: Neither is correct; it is a reflex angle.

    Hint: Recall the precise definitions for each type of angle: acute, right, obtuse, straight, reflex, and complete.

These are 9 of the 60 questions available for Lines & Angles. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.