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Class 6 Maths: Lines and Angles, 8 practice questions with answers

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These are 8 practice questions on Chapter 2, Lines and Angles, of the new NCERT Class 6 Maths textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover rays, naming an angle by its vertex, why longer arms do not make a bigger angle, lines drawn round a full turn, three angles on a straight line, reading the right protractor scale, fractions of a turn as types of angles, and adding angles that share a vertex. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, apart from 90°, 180° and 360°, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 6, Chapter 2, printed pages 13 to 54):

2.1 to 2.4 Point, line segment, line and ray

Question 1. Points P, Q and R lie on a straight line, in that order. Asha says that ray QP and ray QR are the same ray, "because both start at Q". Find her mistake. What angle do the two rays make?

Answer: they are different rays, and they make a straight angle of 180°. A ray is named by its starting point and then a point it passes through, so both rays start at Q, but ray QP goes on towards P and ray QR goes on towards R, in the opposite direction. Two rays from the same point in opposite directions lie along one line, so ∠PQR is a straight angle, which measures 180°. (Rays, page 15; straight angle, page 27; 180°, page 33.)

2.5 Angle

Question 2. An angle has its vertex at K and its arms along rays KM and KN. Ravi names it ∠MNK. Find his mistake and give two correct names.

Answer: the vertex must be the middle letter; the angle is ∠MKN, or ∠NKM. In the name of an angle, the vertex is always written in the middle, with a point on each arm on either side. ∠MNK would mean an angle whose vertex is N, a different angle altogether. The correct names are ∠MKN and ∠NKM. (Naming angles, page 17.)

2.6 and 2.7 Comparing angles and rotating arms

Question 3. Neha draws ∠A = 59° with arms 2 cm long and ∠B = 57° with arms 8 cm long. She says ∠B is the bigger angle because its arms are longer. Is she right?

Answer: no; ∠A is bigger, by 2°. The size of an angle is the amount of turn from one arm to the other, not the length of the arms. 59° is more turn than 57°, so ∠A is bigger, even though its arms are shorter. The book's slit activity shows the same thing: whether rotating arms pass through a slit depends only on the angle between them, not on their length. Two angles this close are hard to compare by eye; superimpose them, vertex on vertex, or measure them. (Size of an angle, page 18; the slit activity, page 26; superimposition, page 22.)

2.8 Special types of angles

Question 4. Points A, O and B lie on a straight line. Rays OC and OD are drawn on the same side of it, with ∠AOC = 56° and ∠DOB = 61°. Rohit says, 'Both of these are acute, so ∠COD must be obtuse.' Find ∠COD and say whether Rohit is right.

Answer: ∠COD = 63°, which is acute, so Rohit is wrong. The three angles on a straight line add up to 180°: ∠COD = 180° − 56° − 61° = 63°, which is less than 90°. (Angles on a straight line, page 27; 180°, page 33; acute, page 31.)

2.9 Measuring angles

Question 5. In a circular rangoli, straight lines are drawn from the centre so that every two neighbouring lines make an angle of 5°, all the way round. Asha says there are 71 lines. How many lines are there, and what was her mistake?

Answer: 72 lines. A full turn is 360°, so the number of 5° angles that fit round the centre is 360 ÷ 5 = 72. Going round, each line starts one 5° angle, and the last angle ends on the first line, so there are as many lines as angles: 72, not 71. (Asha counted as if the lines were on a straight line, where there is one more mark than there are gaps; round a full turn, the first and last lines are the same.) Check: 72 × 5° = 360°. (A full turn is 360°, page 33; dividing the circle into equal parts, page 34.)

Question 6. Kabir places his protractor with its centre on the vertex of an angle and one arm along the 0 mark of the scale that starts on the left. The other arm crosses the protractor where the marks read 66 on one scale and 114 on the other. The angle opens wider than a right angle. What is its measure?

Answer: 114°. The reading must be taken on the scale whose 0 lies on the first arm, the one that starts on the left; counting up from that 0, the other arm is at 114°. The other number, 66, belongs to the scale that starts from 0 on the right, which is not on an arm of this angle. A quick check: the angle opens wider than a right angle, so its measure must be more than 90°, which 114° is and 66° is not. (Two sets of numbers on a protractor, page 36; placing the protractor, page 37.)

2.10 and 2.11 Drawing angles; types of angles and their measures

Question 7. Find each angle in degrees, and say whether it is acute, obtuse or reflex: (a) one-fifth of a full turn, (b) two-fifths of a full turn, (c) three-fifths of a full turn.

Answer: (a) 72°, acute; (b) 144°, obtuse; (c) 216°, reflex. A full turn is 360°. (a) 360° ÷ 5 = 72°, between 0° and 90°: acute. (b) 2 × 72° = 144°, between 90° and 180°: obtuse. (c) 3 × 72° = 216°, between 180° and 360°: reflex. (A full turn is 360°, page 33; types of angles by measure, pages 50 and 51.)

Question 8. Four rays OA, OB, OC and OD start from O, in that order, with ∠AOB = 56°, ∠BOC = 13° and ∠COD = 64°. Name all six angles that two of these rays make (measured the short way, between the rays), find each measure, and say which of them is obtuse.

Answer: ∠AOB = 56°, ∠BOC = 13°, ∠COD = 64°, ∠AOC = 69°, ∠BOD = 77°, ∠AOD = 133°; only ∠AOD is obtuse. An angle's measure is the number of 1° units inside it, so angles that sit side by side at the same vertex add up. ∠AOC = 56° + 13° = 69°, ∠BOD = 13° + 64° = 77° and ∠AOD = 56° + 13° + 64° = 133°. Every angle is less than 90° except ∠AOD = 133°, which is between 90° and 180°, so it is the only obtuse angle. (Naming angles, page 17; the measure as a count of 1° units, page 33; acute and obtuse, pages 50 and 51.)

Questions students ask

What is a ray, and how is it different from a line segment? A line segment has two end points and is the shortest path between them. A ray has only one end point, its starting point, and goes on forever in one direction, like a beam of light from a torch. (Pages 14 and 15.)

What are the types of angles in Class 6 Maths? By measure: acute (more than 0° and less than 90°), right (exactly 90°), obtuse (more than 90° and less than 180°), straight (180°) and reflex (more than 180° and less than 360°). (Pages 27 to 31 and 50 to 51; summary, page 54.)

How do you use a protractor? Put the centre of the protractor on the vertex, line up one arm with the 0° mark, and read the number where the other arm crosses, on the scale that starts from that 0. To draw an angle, draw one arm, put the centre on its end with the arm on 0°, mark the measure, and join. (Measuring, pages 36 and 37; drawing, pages 46 and 47.)

How do you compare two angles by superimposition? Trace one angle and place it on the other so the vertices match and one pair of arms lies on top of each other. The angle whose other arm is outside is the larger; if both arms match, the angles are equal. (Page 22.)

What is a reflex angle? An angle greater than a straight angle and less than a full turn, that is, more than 180° and less than 360°. (Page 51.)

Where are the extra questions for Lines and Angles? The 8 questions above are extra practice on the whole chapter, with worked answers and pages. Printable Class 6 worksheets are linked below.

Which part is "exercise 2.6"? The new Ganita Prakash book has no numbered exercises. 2.6 is a section, Comparing Angles (page 21), and its practice set is the "Figure it Out" on page 23. NCERT's own answers to the sets are printed after the chapter in the same PDF.

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 12.

The facts are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.