Lines and Angles — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Lines and Angles" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Lines and Angles" — 8 important questions with detailed answers for CBSE board exam…
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NCERT Solutions for Class 6 Mathematics — Lines and Angles. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Lines and Angles — All 8 Questions Solved
Q1. What is the difference between a line, a ray, and a line segment?
Step 1: Understand each term
A line segment: has two endpoints and is finite (limited length)
Example: AB with points A and B as endpoints
Step 2: A ray: has one endpoint and extends infinitely in one direction
Example: Ray AB starts at A and goes through B and continues forever
Step 3: A line: has no endpoints and extends infinitely in both directions
Example: Line AB extends forever in both directions past A and past B
Answer: A line segment has 2 endpoints and fixed length. A ray has 1 endpoint and extends one direction infinitely. A line has no endpoints and extends infinitely in both directions.
Q2. How many angles are formed when two lines intersect?
When two lines intersect (cross each other), they create angles at the intersection point.
Step 1: Visualize two lines crossing
Step 2: Count all angles formed at the point where they cross
There are 4 angles formed
Step 3: These 4 angles consist of:
- 2 pairs of opposite angles (called vertically opposite angles)
- Adjacent angles that add up to 180°
Answer: 4 angles are formed. These include 2 pairs of equal opposite angles.
Q3. What type of angle is 90°? Name two other types of angles.
Step 1: Identify the angle type for 90°
90° is called a right angle
Step 2: Name other angle types
An acute angle is less than 90° (between 0° and 90°)
Example: 45°, 60°, 75°
Step 3: Another type
An obtuse angle is between 90° and 180°
Example: 120°, 135°, 150°
Answer: 90° is a right angle. Two other types are: acute angle (less than 90°) and obtuse angle (between 90° and 180°)
Q4. Draw and label a line segment PQ. How many points lie on segment PQ?
Step 1: A line segment PQ has two endpoints P and Q
Step 2: Between P and Q, there are infinitely many points
Step 3: In addition to the endpoints, any point you mark on the segment between P and Q is considered to lie on PQ
Example: If we mark point R between P and Q, then R lies on PQ
Answer: A line segment has infinitely many points (including the two endpoints). Every point on the segment lies on PQ.
Q5. If two angles are complementary, and one angle is 35°, what is the other angle?
Two complementary angles are two angles whose sum is 90°.
Step 1: Set up the equation
Angle 1 + Angle 2 = 90°
Step 2: Substitute the known angle
35° + Angle 2 = 90°
Step 3: Solve for the unknown angle
Angle 2 = 90° - 35°
Angle 2 = 55°
Step 4: Verify: 35° + 55° = 90° ✓
Answer: The other angle is 55°
Q6. What is a reflex angle? Give an example measure.
Step 1: Define a reflex angle
A reflex angle is an angle that is greater than 180° but less than 360°
Step 2: Compare with other angles
Acute angle: less than 90°
Right angle: equals 90°
Obtuse angle: between 90° and 180°
Reflex angle: between 180° and 360°
Step 3: Give examples of reflex angles
200°, 270°, 315°, 350°
Answer: A reflex angle is an angle greater than 180° and less than 360°. Example: 270° or 225°
Q7. If two angles form a linear pair, they are supplementary. If one angle is 120°, what is the other?
Two supplementary angles are two angles whose sum is 180°. A linear pair consists of two adjacent angles on a straight line.
Step 1: Set up the equation for supplementary angles
Angle 1 + Angle 2 = 180°
Step 2: Substitute the known angle
120° + Angle 2 = 180°
Step 3: Solve for the unknown angle
Angle 2 = 180° - 120°
Angle 2 = 60°
Step 4: Verify: 120° + 60° = 180° ✓
Answer: The other angle is 60°
Q8. Can two acute angles be supplementary? Explain why or why not.
Supplementary angles must sum to 180°. An acute angle is less than 90°.
Step 1: Consider two acute angles
Let Angle 1 = any angle less than 90° (say 45°)
Let Angle 2 = any angle less than 90° (say 50°)
Step 2: Find their sum
45° + 50° = 95°
Step 3: For any two acute angles
Maximum sum = 90° + 90° = 180° (but these are right angles, not acute)
If both angles are less than 90°, the sum is always less than 180°
Step 4: Conclusion
Since acute angles are each less than 90°, their sum is always less than 180°
Answer: No, two acute angles cannot be supplementary because their sum will always be less than 180°.
Lines and Angles — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. A part of a line with two endpoints is called a:
- A. Line
- B. Ray
- C. Line segment
- D. Angle
Answer: C. Line segment — A line segment is a part of a line that has two distinct endpoints and a definite length.
MCQ 2. An angle that measures exactly 90 degrees is called a:
- A. Acute angle
- B. Obtuse angle
- C. Right angle
- D. Straight angle
Answer: C. Right angle — A right angle is defined as an angle that measures exactly 90 degrees.
MCQ 3. How many arms does an angle have?
- A. One
- B. Two
- C. Three
- D. Four
Answer: B. Two — An angle is formed by two rays sharing a common endpoint, and these two rays are called the arms of the angle.
MCQ 4. When two rays meet at a common endpoint, what do they form?
- A. A line
- B. A line segment
- C. An angle
- D. A point
Answer: C. An angle — An angle is formed when two rays originate from the same common endpoint, which is called the vertex.
MCQ 5. Which of the following best describes parallel lines?
- A. Lines that meet at a single point
- B. Lines that never intersect
- C. Lines that form a 90-degree angle
- D. Lines that are curved
Answer: B. Lines that never intersect — Parallel lines are lines that are always the same distance apart and never meet, no matter how far they are extended.
MCQ 6. What is the complement of an angle that measures 40 degrees?
- A. 50 degrees
- B. 140 degrees
- C. 90 degrees
- D. 180 degrees
Answer: A. 50 degrees — Two angles are complementary if their sum is 90 degrees. Therefore, the complement of 40 degrees is 90 - 40 = 50 degrees.
MCQ 7. What is the supplement of an angle that measures 110 degrees?
- A. 70 degrees
- B. 90 degrees
- C. 180 degrees
- D. 20 degrees
Answer: A. 70 degrees — Two angles are supplementary if their sum is 180 degrees. Therefore, the supplement of 110 degrees is 180 - 110 = 70 degrees.
MCQ 8. If two lines cross each other at a single point, they are called:
- A. Parallel lines
- B. Perpendicular lines
- C. Intersecting lines
- D. Coincident lines
Answer: C. Intersecting lines — Intersecting lines are two or more lines that meet or cross each other at a common point.
MCQ 9. What type of angle is formed by the hands of a clock at 3 o'clock?
- A. Acute angle
- B. Obtuse angle
- C. Right angle
- D. Straight angle
Answer: C. Right angle — At 3 o'clock, the hour hand points to 3 and the minute hand points to 12. These two hands form a 90-degree angle, which is a right angle.
MCQ 10. An angle that measures exactly 180 degrees is called a:
- A. Right angle
- B. Obtuse angle
- C. Straight angle
- D. Reflex angle
Answer: C. Straight angle — A straight angle is formed when two rays point in opposite directions, forming a straight line, and it measures exactly 180 degrees.
MCQ 11. If two lines intersect and form a right angle at their point of intersection, what are they called?
- A. Parallel lines
- B. Intersecting lines
- C. Perpendicular lines
- D. Oblique lines
Answer: C. Perpendicular lines — Perpendicular lines are two lines that intersect each other to form a 90-degree (right) angle.
MCQ 12. If an angle is twice its complement, what is the measure of the angle?
- A. 30 degrees
- B. 60 degrees
- C. 45 degrees
- D. 90 degrees
Answer: B. 60 degrees — Let the angle be 'x'. Its complement is (90-x). If x = 2 * (90-x), then x = 180 - 2x. Adding 2x to both sides gives 3x = 180, so x = 60 degrees.
MCQ 13. If an acute angle is added to an obtuse angle, the sum will always be:
- A. An acute angle
- B. An obtuse angle
- C. A straight angle
- D. Cannot be determined without specific values
Answer: D. Cannot be determined without specific values — An acute angle is less than 90 degrees, and an obtuse angle is between 90 and 180 degrees. Their sum could be obtuse, straight, or even a reflex angle (greater than 180 degrees), depending on the specific measures.
MCQ 14. Which of the following statements is TRUE?
- A. All intersecting lines are perpendicular lines
- B. Parallel lines always meet at infinity
- C. A ray has one endpoint
- D. A line segment extends indefinitely in one direction
Answer: C. A ray has one endpoint — A ray starts at a point and extends infinitely in one direction, meaning it has exactly one endpoint. The other statements are false.
MCQ 15. Two angles form a linear pair. If one angle measures 75 degrees, what is the measure of the other angle?
- A. 15 degrees
- B. 105 degrees
- C. 180 degrees
- D. 90 degrees
Answer: B. 105 degrees — Angles in a linear pair are supplementary, which means their sum is always 180 degrees. If one angle is 75 degrees, the other is 180 - 75 = 105 degrees.
MCQ 16. What is a point in geometry?
- A. A mark of position
- B. A thick dot
- C. A line with no end
- D. A curved line
Answer: A. A mark of position — A point is a basic unit in geometry that represents an exact location or position and has no dimension.
MCQ 17. How many endpoints does a line segment have?
- A. Zero
- B. One
- C. Two
- D. Infinite
Answer: C. Two — A line segment is a part of a line that has two distinct endpoints and includes all the points on the line between them.
MCQ 18. Which of the following describes a ray?
- A. A line with two endpoints.
- B. A line that extends indefinitely in both directions.
- C. A part of a line that extends indefinitely in one direction from a single endpoint.
- D. A collection of points forming a curve.
Answer: C. A part of a line that extends indefinitely in one direction from a single endpoint. — A ray has one endpoint and extends infinitely in one direction, unlike a line segment which has two endpoints or a line which extends infinitely in both directions.
MCQ 19. Which pair of lines will never intersect, no matter how far they are extended?
- A. Intersecting lines
- B. Perpendicular lines
- C. Parallel lines
- D. Skew lines
Answer: C. Parallel lines — Parallel lines are lines in a plane that are always the same distance apart and never intersect each other.
MCQ 20. When two lines intersect, how many common points do they share?
- A. Zero
- B. One
- C. Two
- D. Infinite
Answer: B. One — Intersecting lines share exactly one common point, which is called the point of intersection.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.