CBSE Class 6 Mathematics Symmetry Practice Paper Assignment Set 04 with Answers

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CBSE Class 6 Mathematics Ganita Prakash Chapter 9 Symmetry Practice Paper 28 has 20 questions for 40 marks across Sections A to E, and each one is answered below with full working. The questions ask you to work back from the smallest angle to the number of sides (such as 40° for a nonagon), explain why a square matches after 270°, test turns of 180°, 216° and 300° on decagons, pentagons and hexagons, compare the circle's order with polygons, and solve case studies on octagonal playground tiles and equilateral-triangle festival badges.

Section A: Multiple Choice Questions (1 Mark Each)

Question 1: A regular triangle is rotated about its center. After how many degrees of rotation does it first look exactly the same as its original position?
(a) 60°
(b) 90°
(c) 120°
(d) 180°
Show Answer & Explanation

Answer: (c) 120°

Explanation:
1. A regular triangle is an equilateral triangle; it looks the same 3 times in one full turn.
2. The first match comes after 360° ÷ 3 = 120°.
3. At 60°, 90° or 180° a vertex points where a side used to be, so it does not match.

Teacher's Note:
1. A 180° turn turns an equilateral triangle upside down, so it does not match.
2. Smallest angle = 360° ÷ order.

Question 2: A regular polygon matches itself exactly 8 times during one full rotation. How many sides does the polygon have?
(a) 6
(b) 7
(c) 8
(d) 9
Show Answer & Explanation

Answer: (c) 8

Explanation:
1. The number of matches in one full turn is the order of rotational symmetry, here 8.
2. For a regular polygon, the order equals the number of sides.
3. So the polygon has 8 sides (a regular octagon).

Teacher's Note:
1. This rule works only for regular polygons.
2. Its smallest angle would be 360° ÷ 8 = 45°.

Question 3: A regular polygon has the smallest rotational symmetry angle equal to 40°. How many sides does the polygon have?
(a) 7
(b) 8
(c) 9
(d) 10
Show Answer & Explanation

Answer: (c) 9

Explanation:
1. Number of sides = order = 360° ÷ smallest angle.
2. 360° ÷ 40° = 9.
3. The polygon has 9 sides (a regular nonagon).

Teacher's Note:
1. Check: 9 × 40° = 360°.
2. 8 sides would give 45° and 10 sides 36°.

Question 4: A square is rotated by 270°. Why does it exactly match its original position?
(a) 270° is greater than 180°
(b) 270° is a multiple of its 90° angle of rotation
(c) A square has 4 equal sides
(d) 270° is a full rotation
Show Answer & Explanation

Answer: (b) 270° is a multiple of its 90° angle of rotation

Explanation:
1. A square's smallest angle of rotation is 90°, so it matches after 90°, 180°, 270° and 360°.
2. 270° ÷ 90° = 3, so a 270° turn is three quarter turns, and each quarter turn gives a match.
3. The reason is that 270° is a multiple of its 90° angle of rotation.

Teacher's Note:
1. (a) is not a reason: 200° is also more than 180° but the square does not match.
2. (d) is false: a full rotation is 360°.

Question 5: Which regular polygon has the smallest rotational symmetry angle equal to 45°?
(a) Pentagon
(b) Hexagon
(c) Octagon
(d) Decagon
Show Answer & Explanation

Answer: (c) Octagon

Explanation:
1. Number of sides = 360° ÷ 45° = 8.
2. A regular polygon with 8 sides is an octagon.
3. Pentagon gives 72°, hexagon 60° and decagon 36°.

Teacher's Note:
1. Learn the pairs: 3–120°, 4–90°, 5–72°, 6–60°, 8–45°, 10–36°.
2. Check: 8 × 45° = 360°.

Question 6: Which regular polygon matches itself after a rotation of 72°?
(a) Square
(b) Pentagon
(c) Hexagon
(d) Octagon
Show Answer & Explanation

Answer: (b) Pentagon

Explanation:
1. A regular polygon matches after its smallest angle and after every multiple of it.
2. Smallest angles: square 90°, pentagon 72°, hexagon 60°, octagon 45°.
3. 72° is a multiple only of the pentagon's angle (72° = 1 × 72°), so the answer is the pentagon.

Teacher's Note:
1. 72° is not a multiple of 90°, 60° or 45°, so the other shapes do not match.
2. 360° ÷ 72° = 5.

Question 7: When a regular hexagon is rotated by 300°, what will happen?
(a) It will not match
(b) It will partially match
(c) It will match exactly
(d) Its size will change
Show Answer & Explanation

Answer: (c) It will match exactly

Explanation:
1. The smallest angle of a regular hexagon is 360° ÷ 6 = 60°.
2. 300° ÷ 60° = 5, a whole number, so 300° is 5 steps of 60°.
3. So it will match exactly.

Teacher's Note:
1. Turning by 300° one way is the same as turning by 60° the other way.
2. Rotation never changes size.

Question 8: Which of the following shapes has the highest order of rotational symmetry?
(a) Triangle
(b) Square
(c) Pentagon
(d) Circle
Show Answer & Explanation

Answer: (d) Circle

Explanation:
1. Even taking the regular forms, a triangle has order 3, a square 4 and a regular pentagon 5.
2. A circle matches itself after a turn through any angle, so it has infinitely many matching positions.
3. So the circle has the highest order.

Teacher's Note:
1. The order of a polygon can never be more than its number of sides.
2. A circle's order is said to be infinite.

Question 9:
Assertion (A): Regular polygons always have rotational symmetry.
Reason (R): All sides and all angles of a regular polygon are equal.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Assertion: every regular polygon with n sides matches itself after a turn of 360° ÷ n, which is less than 360°. A is true.
2. Reason: a regular polygon is defined as one with all sides equal and all angles equal. R is true.
3. Because the sides and angles are all equal, turning one vertex onto the next makes the whole figure fit exactly, so R explains A.

Teacher's Note:
1. A rhombus has equal sides but unequal angles; it has order 2, not 4.
2. Both equal sides and equal angles are needed for order n.

Question 10:
Assertion (A): The order of rotational symmetry of a regular decagon is 10.
Reason (R): A regular decagon has 10 equal sides.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Assertion: a regular decagon matches itself after every 36°, which happens 10 times in a full turn. A is true.
2. Reason: a decagon has 10 sides, and in a regular decagon they are all equal. R is true.
3. The order of a regular polygon equals its number of equal sides, so R correctly explains A.

Teacher's Note:
1. Order of rotational symmetry of a regular polygon = number of sides.
2. Smallest angle of a regular decagon: 360° ÷ 10 = 36°.

Section B: Short Answer Questions (2 Marks Each)

Question 11. A regular polygon has 6 equal sides.
(a) What is the order of rotational symmetry of the polygon?
(b) What is the smallest angle of rotation for which it matches itself?
Answer:
(a) The polygon is a regular hexagon, and its order equals its number of sides: 6.
(b) Smallest angle of rotation = 360° ÷ 6 = 60°.
In simple words: A regular hexagon has order 6 and matches every 60°.

Teacher's Note:
1. Order × smallest angle = 360°.
2. 6 × 60° = 360°.

 

Question 12. A regular polygon has 10 equal sides.
(a) What is the order of rotational symmetry of the polygon?
(b) What is the smallest angle of rotation for which it matches itself?
Answer:
(a) It is a regular decagon, so the order of rotational symmetry is 10.
(b) Smallest angle of rotation = 360° ÷ 10 = 36°.
In simple words: A regular decagon has order 10 and matches every 36°.

Teacher's Note:
1. More sides means a smaller smallest angle.
2. 10 × 36° = 360°.

 

Question 13. A regular polygon has the smallest rotational symmetry angle equal to 90°.
(a) What is the order of rotational symmetry of the polygon?
(b) Identify the name of the polygon.
Answer:
(a) Order = 360° ÷ 90° = 4.
(b) A regular polygon with 4 sides is a square.
In simple words: Matching every 90° means order 4, so the regular polygon is a square.

Teacher's Note:
1. A rectangle is not regular; its smallest angle is 180°.
2. 4 × 90° = 360°.

 

Question 14. A regular polygon has rotational symmetry of order 3.
(a) What is the smallest angle of rotation?
(b) Identify the name of the polygon.
Answer:
(a) Smallest angle = 360° ÷ 3 = 120°.
(b) A regular polygon with 3 sides is an equilateral triangle.
In simple words: Order 3 means a match every 120°; the shape is an equilateral triangle.

Teacher's Note:
1. A 'regular triangle' and an 'equilateral triangle' are the same shape.
2. 3 × 120° = 360°.

 

Section C: Short Answer Questions (3 Marks Each)

Question 15. A regular decagon is rotated about its center.
(a) What is the order of rotational symmetry of the decagon?
(b) What is the smallest angle of rotation?
(c) Will the decagon match its original position after a rotation of 180°? Justify your answer.
Answer:
(a) A regular decagon has 10 sides, so its order of rotational symmetry is 10.
(b) Smallest angle of rotation = 360° ÷ 10 = 36°.
(c) 180° ÷ 36° = 5, a whole number, so 180° is exactly 5 steps of 36°. Yes, it matches after 180°.
O 36° 72° 108° 144° 180° 216° 252° 288° 324° 360° A Regular decagon: a match every 36° (180° after 5 steps)
In simple words: 180° is 5 steps of 36°, so the decagon matches after a half turn.

Teacher's Note:
1. A turn matches when it is a whole-number multiple of the smallest angle.
2. Any regular polygon with an even number of sides matches after 180°.

 

Question 16. A regular octagon is rotated step by step.
(a) What is the order of rotational symmetry?
(b) What will be the angle of rotation after 4 matching positions?
(c) Will the octagon match its original position after this rotation?
Answer:
(a) A regular octagon has 8 sides, so its order of rotational symmetry is 8; it matches every 360° ÷ 8 = 45°.
(b) After 4 matching positions the angle turned = 4 × 45° = 180°.
(c) Yes. 180° is a multiple of 45° (it is the 4th matching position), so the octagon matches its original position.
In simple words: Four steps of 45° make 180°, and the octagon matches there.

Teacher's Note:
1. Angle after k matches = k × smallest angle.
2. The octagon's 4th match is a half turn.

 

Question 17. A regular pentagon is rotated about its center.
(a) What is the smallest angle of rotation?
(b) Will it match after a rotation of 216°?
(c) What is the order of rotational symmetry?
Answer:
(a) Smallest angle of rotation = 360° ÷ 5 = 72°.
(b) 216° ÷ 72° = 3, a whole number (216° = 3 × 72°). Yes, it matches after 216°.
(c) It matches at 72°, 144°, 216°, 288° and 360°, so the order is 5.
In simple words: 216° is three 72° steps, so the pentagon matches; its order is 5.

Teacher's Note:
1. A regular pentagon does not match after 180°, because 180 is not a multiple of 72.
2. 5 × 72° = 360°.

 

Section D: Long Answer Question (5 Marks)

Question 18. A regular hexagon is rotated continuously about its center.
(a) What is the order of rotational symmetry of the hexagon?
(b) What is the smallest angle of rotation?
(c) Will it match after a rotation of 120°? Justify.
(d) Will it match after a rotation of 240°? Justify.
(e) How many times will it match itself during one complete rotation?
Answer:
(a) A regular hexagon has 6 sides, so its order of rotational symmetry is 6.
(b) Smallest angle of rotation = 360° ÷ 6 = 60°.
(c) 120° ÷ 60° = 2, a whole number, so 120° is 2 steps of 60°. Yes, it matches.
(d) 240° ÷ 60° = 4, a whole number, so 240° is 4 steps of 60°. Yes, it matches.
(e) It matches at 60°, 120°, 180°, 240°, 300° and 360°: 6 times.
O 60° 120° 180° 240° 300° 360° A Regular hexagon: matching positions every 60°
In simple words: A regular hexagon matches every 60°, so 120° and 240° both work and there are 6 matches.

Teacher's Note:
1. Divide the given angle by the smallest angle; a whole number means a match.
2. The number of matches in a full turn equals the order.
3. Read 120° and 240° on the figure: both are vertices.

 

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: School Hall Floor Design
In a modern school playground, decorative tiles shaped like regular octagons are arranged around a circular sitting area. Students observe these tiles while sitting and notice that the shape looks exactly the same after certain rotations. One student brings a paper model of the tile and rotates it slowly about its center. The student marks positions where the tile matches its original shape and measures the angle between these positions using a protractor. The teacher explains that this matching occurs due to rotational symmetry. Students learn that the number of matching positions depends on the number of sides of the regular polygon used.
Based on the above, answer the following questions:
(a) What is the order of rotational symmetry of the regular octagon tile?
(b) What is the smallest angle of rotation for which the tile matches itself?
(c) Will the tile match its original position after a rotation of 135°? Show the calculation.
(d) How many times will the tile match itself during one complete rotation of 360°?
Answer:
(a) The order of a regular octagon = number of sides = 8.
(b) Smallest angle = 360° ÷ 8 = 45°.
(c) 135° ÷ 45° = 3, a whole number, so 135° = 3 × 45°. Yes, the tile matches after 135°.
(d) In one complete rotation the tile matches 8 times.
In simple words: The octagon tile matches every 45°, so 135° (3 steps) works and there are 8 matches.

Teacher's Note:
1. The angle between neighbouring matching positions measured with a protractor is 45°.
2. 8 × 45° = 360°.

 

Question 20. Case Study 2:
During the annual cultural festival, students design decorative badges shaped like regular equilateral triangles. These badges are attached to their uniforms. Curious about symmetry, students rotate a paper badge about its center and observe matching positions. They carefully mark each matching position and measure the angles between them using a protractor. They notice equal angle intervals between matches. The mathematics teacher explains that regular polygons show rotational symmetry and that the number of matches equals the number of sides. Students realize how symmetry helps designers create balanced logos, decorations, and artistic patterns used in school festivals and real-life creative designs everywhere.
Based on the above, answer the following questions:
(a) What is the order of rotational symmetry of the equilateral triangle badge?
(b) What is the smallest angle of rotation for which the badge matches itself?
(c) Will the badge match its original position after a rotation of 240°? Show the calculation.
(d) How many times will the badge match itself during one full rotation of 360°?
Answer:
(a) An equilateral triangle has 3 equal sides, so the order of rotational symmetry is 3.
(b) Smallest angle = 360° ÷ 3 = 120°.
(c) 240° ÷ 120° = 2, a whole number, so 240° = 2 × 120°. Yes, the badge matches after 240°.
(d) It matches at 120°, 240° and 360°: 3 times in one full rotation.
O 120° 240° 360° A Triangle badge: matches at 120°, 240° and 360°
In simple words: The triangle badge matches every 120°, so it matches at 240° and 3 times in all.

Teacher's Note:
1. The equal angle intervals the students measured are each 120°.
2. 3 × 120° = 360°.

 

Free study material for Mathematics

Download Practice Assignments: Class 6 Mathematics Chapter 09 Symmetry

Chapter Practice Questions for Class 6 Mathematics

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