CBSE Class 6 Mathematics Symmetry Worksheet Set 08

Long Answer Questions

Question 1. Look at the kinds of pictures with which this chapter opens: a butterfly, a flower, a rangoli, a paper pinwheel and a patch of clouds.
(i) What do we mean when we say that a figure has symmetry?
(ii) Which of these five pictures are symmetrical and which one is not? Give a reason for your answer about the clouds.
(iii) The butterfly has one line of symmetry while the pinwheel has none. Does this mean that the pinwheel is not symmetrical at all? Explain.
(iv) Name one famous Indian building that has a line of symmetry and say where the line lies.
Answer:
(i) A figure has symmetry when it is made of parts that repeat in a definite pattern. The repeat can be seen by folding the figure or by turning it.
(ii) The butterfly, flower, rangoli and pinwheel are symmetrical. The clouds are not: the puffs and edges are all of different shapes and sizes, so nothing repeats in a definite pattern, and neither a fold nor a turn brings the picture back onto itself.
(iii) No, the pinwheel is still symmetrical. Its blades all bend the same way, so no fold works, but when it is turned through 90° about its pin it looks exactly the same. So it has rotational symmetry instead of reflection symmetry. The butterfly is the other way round: one line of symmetry but no rotational symmetry. The flower and the rangoli have both kinds.
(iv) The Taj Mahal. Its line of symmetry is the vertical line through the middle of the main dome and the main gateway; the left half is the mirror image of the right half.
In simple words: Symmetry means a definite repeat; the pinwheel repeats by turning, the butterfly by folding, and clouds not at all.

Teacher's Note:
1. There are two kinds of symmetry: reflection and rotation.
2. A figure needs only one kind to be symmetrical.
3. Other symmetrical buildings may be named too.

Teacher's Note:
1. Fill the table by imagining folds and turns.
2. The parallelogram is the odd one out.
3. Countless means infinitely many.

Question 3. The six-pointed star tile shown below is cut out of card. The red dot is at its centre, and its six points are all alike and equally spaced.
(i) Trace the tile and draw all its lines of symmetry. How many are there, and of how many kinds?
(ii) Describe two different folds that show two of these lines.
(iii) Write the order of rotational symmetry of the tile and all its angles of symmetry.
Answer:
(i) The star has 6 lines of symmetry, all passing through the red centre dot. They are of two kinds:
3 lines, each joining one point of the star to the opposite point;
3 lines, each joining one inner corner (the valley between two points) to the opposite inner corner.
(ii) Fold along the vertical line through the top point and the bottom point: the three points on the left fall exactly on the three points on the right. Fold along the horizontal line through the two side valleys: the three upper points fall exactly on the three lower points. Both folds give exact overlap, so both are lines of symmetry.
(iii) The six points are alike and equally spaced, so each point takes the place of the next after a turn of 360° ÷ 6 = 60°. The angles of symmetry are 60°, 120°, 180°, 240°, 300° and 360°, and the order of rotational symmetry is 6, the same as the number of lines of symmetry.
In simple words: The six-pointed star has 6 lines (3 through points, 3 through valleys) and order 6 with smallest angle 60°.

Teacher's Note:
1. Draw lines through points and through valleys separately.
2. All lines of symmetry pass through the centre.
3. 60° comes from 360° ÷ 6.

Question 4. A square sheet has its corners marked P (top left), Q (top right), R (bottom right) and S (bottom left).
(i) What is meant by reflection symmetry?
(ii) The square is reflected in its vertical line of symmetry. Where do P, Q, R and S go?
(iii) The square is reflected in the diagonal through P and R. Which corners stay where they are and which two exchange places?
(iv) The square is reflected in its horizontal line of symmetry. Write the new position of each corner.
Answer:
(i) When a figure is folded along a line of symmetry, the part on one side falls exactly on the part on the other side. Each point on one side is reflected by the line to a matching point on the other side, like an image in a mirror. A figure with one or more lines of symmetry has reflection symmetry.
(ii) The vertical line passes through the middles of the top and bottom sides. P and Q exchange places, and S and R exchange places. So P goes to Q's position, Q to P's, R to S's and S to R's.
(iii) P and R lie on the diagonal, so they stay where they are. Q and S exchange places.
(iv) The horizontal line passes through the middles of the left and right sides. The top corners go down and the bottom corners come up: P goes to S's place, S to P's, Q to R's and R to Q's.
In simple words: In each reflection, corners on the mirror line stay and the others swap with their mirror partners.

Teacher's Note:
1. Draw the square and the mirror line each time.
2. Points on the mirror line never move.
3. Corners swap in pairs.

Question 5. Half of a design is drawn on a dot grid. The dashed blue line is to be a line of symmetry of the finished design.
(i) Describe step by step the method you will use to draw the missing half on a dot grid.
(ii) Describe the shape of the completed design.
(iii) How many lines of symmetry does the completed design have, and what is its order of rotational symmetry?
Answer:
(i) Work corner by corner:
Copy the given half and the dashed line on your own dot grid.
Take one corner of the given half and count how many dot spaces it is from the dashed line.
On the other side of the dashed line, count the same number of spaces at the same level and mark a dot. This is the mirror point of that corner.
Do this for every corner. Points already on the dashed line do not move.
Join the new dots in the same order as the old corners were joined.
Check by folding the sheet along the dashed line: the two halves must cover each other exactly.
(ii) The completed design looks like a stepped hill (or a tree): a wide flat base 6 spaces long, two equal steps climbing up on the left and two matching steps on the right, and a point at the top where the two slanting edges meet on the dashed line.
(iii) It has exactly 1 line of symmetry, the dashed line. Turning it does not bring it back before a full turn, because the top is a point while the bottom is a flat base. So its only angle of symmetry is 360°, its order of rotational symmetry is 1, and it has no rotational symmetry.
In simple words: Mirror each corner across the dashed line by counting dots; the result is a stepped hill with 1 line of symmetry and no rotational symmetry.

Teacher's Note:
1. Counting dots keeps distances exact.
2. Keep each mirror point at the same level.
3. A figure can have a line of symmetry but no rotational symmetry.

Question 6. Reflection symmetry and rotational symmetry are two different ideas.
(i) Explain each of them in your own words.
(ii) Give one figure that has reflection symmetry but no rotational symmetry.
(iii) Give one figure that has rotational symmetry but no reflection symmetry.
(iv) Give one figure that has both, and write how many of each it has.
Answer:
(i) A figure has reflection symmetry when there is a line such that folding along it makes the two parts cover each other exactly; the line acts like a mirror. A figure has rotational symmetry when it can be turned about a fixed point through an angle less than a full turn and still look exactly the same; the point is the centre of rotation and the turn is an angle of symmetry.
(ii) The capital letter A. The vertical fold through its peak works, so it has 1 line of symmetry, but no turn less than 360° leaves it unchanged.
(iii) A parallelogram that is not a rectangle or a rhombus. It falls on itself after a half turn of 180° (order 2), but no fold works. A paper windmill is another example, with order 4.
(iv) A square: 4 lines of symmetry and order of rotational symmetry 4 (angles 90°, 180°, 270°, 360°). An equilateral triangle also works, with 3 lines and order 3.
In simple words: Reflection is about folding over a line, rotation is about turning about a point; some figures have one, some both.

Teacher's Note:
1. Give a clear example for each case.
2. The square and the windmill are easy examples to remember.

Question 7. A figure is made by drawing three straight arms going outwards from a centre dot, with the same small flag drawn on every arm.
(i) If the three arms are placed at angles that are not equal, the figure comes back to itself only after a full turn. Explain why.
(ii) Show that if such a three-arm figure is to have rotational symmetry, the three angles at the centre must be equal, and find that angle. Then write all its angles of symmetry.
(iii) What must the angle between neighbouring arms be for a four-arm figure and for an eight-arm figure of this kind?
Answer:
(i) The look of the figure depends on the sizes of the gaps between the arms. If the three gaps are of different sizes, then after any turn smaller than a full turn, an arm lands where the gap next to it is a different size from before, so the turned figure does not cover the original. Only a full turn of 360° puts every arm back in its own place.
(ii) Call the three angles at the centre ∠A, ∠B and ∠C, in order. If a turn makes the figure fall on itself, ∠A must land on ∠B, ∠B on ∠C and ∠C on ∠A. Angles that cover each other are equal, so ∠A = ∠B = ∠C.
Together they make a full turn, so each is 360° ÷ 3 = 120°. The angles of symmetry are 120°, 240° and 360°.
(iii) The arms must share a full turn equally: for 4 arms, 360° ÷ 4 = 90°; for 8 arms, 360° ÷ 8 = 45°.
In simple words: Equal arms need equal gaps; the gap is 360° divided by the number of arms.

Teacher's Note:
1. Turning must carry every gap onto an equal gap.
2. Gap = 360° ÷ number of arms.

Question 8. Paper folding, cutting and punching are ways of making symmetric designs.
(i) A square sheet is folded once from left to right and then once from top to bottom. A single hole is punched through the folded sheet. How many holes appear when the sheet is opened, and how are they placed?
(ii) Where are the lines of symmetry of the opened sheet in part (i)?
(iii) The same sheet is folded in the same way. Where should the punch be made in the folded sheet so that the four holes come near the four corners of the opened sheet?
(iv) Instead of the two folds above, the square sheet is folded once along a diagonal and then a shape is cut out. Which line will be a line of symmetry of the opened sheet?
Answer:
(i) The two folds make 4 layers and the punch goes through all of them, so 4 holes appear. They sit at the four corners of a small rectangle: two above the horizontal fold and two below it, two to the left of the vertical fold and two to its right, each hole at the same distance from the folds as its partners.
(ii) The two fold lines: the vertical line through the middle and the horizontal line through the middle. Folding along either makes holes fall on holes.
(iii) In the folded sheet, the closed corner where the two folds meet is the centre of the whole sheet, and the corner opposite to it is made of the four corners of the original sheet. Punch close to that free (opposite) corner; on opening, one hole comes near each corner of the sheet.
(iv) The shape is cut from both layers at once, and the layers are mirror halves about the diagonal. So the diagonal along which the sheet was folded is a line of symmetry of the opened sheet.
In simple words: Each fold doubles the layers and becomes a line of symmetry of the opened sheet.

Teacher's Note:
1. Try this with real paper and a punch.
2. The closed corner of the folded sheet is the centre of the opened sheet.

Question 9. The Ashoka Chakra at the centre of our national flag is a wheel with 24 spokes placed evenly around the hub.
(i) How many lines of symmetry does the Chakra have, and where do they lie?
(ii) What is its order of rotational symmetry and its smallest angle of symmetry?
(iii) A cartwheel has 18 evenly placed spokes. Find its smallest angle of symmetry and its order of rotational symmetry.
(iv) A plain circle, with no spokes drawn, looks the same after a turn through any angle at all. Explain why drawing the 24 spokes cuts the angles of symmetry down from “every angle” to only 24 of them.
Answer:
(i) It has 24 lines of symmetry, all through the centre. The 24 evenly placed spokes make 12 opposite pairs, and each pair lies along one line (12 lines). Another 12 lines pass through the middles of the gaps. In all, 12 + 12 = 24 lines.
(ii) The wheel falls on itself each time one spoke takes the place of the next, which happens 24 times in a full turn. Order = 24, smallest angle = 360° ÷ 24 = 15°. The other angles of symmetry are the multiples of 15° up to 360°.
(iii) Smallest angle = 360° ÷ 18 = 20°, order of rotational symmetry = 18.
(iv) A plain circle has no marks, so any turn leaves it looking the same. Once 24 spokes are drawn, a spoke must land on a spoke. The smallest turn that does this is 15°, and only multiples of 15° work. In one full turn there are just 24 such angles, so the Chakra has 24 angles of symmetry instead of countless many.
In simple words: 24 spokes give 24 lines, order 24 and smallest angle 15°; the spokes limit the turns that work.

Teacher's Note:
1. Lines go through spokes and through gaps.
2. Adding marks to a figure reduces its symmetry.

Question 10. The angles of symmetry of a figure are always the multiples of its smallest angle of symmetry.
(i) Explain why 360° is an angle of symmetry of every figure.
(ii) Explain why the smallest angle of symmetry, when it is a whole number of degrees, must be a factor of 360.
(iii) A figure has exactly 8 angles of symmetry. Write all of them.
(iv) The smallest angle of symmetry of another figure is 12°. How many angles of symmetry does it have in all, and is 150° one of them? Give a reason.
Answer:
(i) A turn of 360° is one complete turn. Every point of the figure goes right round and comes back to where it started, so the figure looks exactly as before. Hence 360° is an angle of symmetry of every figure, even one with no other symmetry.
(ii) Let the smallest angle be a. Turning by a twice gives 2a, three times gives 3a, and so on; all these are angles of symmetry. A full turn of 360° is also one of them, so 360 = k × a for some whole number k. So a is a factor of 360.
(iii) Smallest angle = 360° ÷ 8 = 45°. The eight angles are 45°, 90°, 135°, 180°, 225°, 270°, 315° and 360°.
(iv) Number of angles = 360° ÷ 12° = 30. Now 150 ÷ 12 = 12.5 is not a whole number, so 150° is not a multiple of 12° and is not an angle of symmetry. The nearest ones are 144° and 156°.
In simple words: Angles of symmetry are the multiples of the smallest one up to 360°, so the smallest angle divides 360.

Teacher's Note:
1. Smallest angle × number of angles = 360°.
2. To test an angle, divide it by the smallest angle.

Case Study Based Questions

Question 11. A rangoli competition in school
For Diwali, Class 6 held a rangoli competition in the school verandah. Asha drew her rangoli inside a square. At the centre she drew a small round diya. On the middle of each of the four sides of the square she drew one petal, and all four petals were exactly the same shape and size. Each petal was itself alike on its left and its right. When the judge walked round the rangoli, she said that the design came back to its own look again and again as she moved. Asha was happy, because she had planned the design by turning the same petal around the centre.
(i) Name the fixed point about which Asha’s design is turned.
(ii) What is the smallest angle through which the rangoli can be turned so that it looks exactly the same?
(iii) How many lines of symmetry does the rangoli have?
(iv) Write all the angles of symmetry of the rangoli.
Answer:
(i) The centre of the square, where the diya is drawn. This is the centre of rotation.
(ii) 90° (a quarter turn), because the four petals are alike and each takes the place of the next.
(iii) 4: the two lines joining the middles of opposite sides (through opposite petals) and the two diagonals of the square.
(iv) 90°, 180°, 270° and 360°, so the order of rotational symmetry is 4.
In simple words: Four equal symmetric petals on a square give 4 lines and a smallest turn of 90°.

Teacher's Note:
1. The rangoli has all the symmetries of a square.
2. Each petal being symmetric keeps the lines of symmetry.

Question 12. The ceiling fan in the classroom
The ceiling fan in Class 6 B has three blades fixed to a round hub in the middle. The three blades are of the same shape and size and are fixed at equal distances around the hub. Every blade is bent in the same way, so each blade looks like a wide curved leaf turning towards the right. When the fan is switched off, Mira slowly turns one blade with a stick until the fan looks exactly as it did before. Her teacher tells the class that the fan is a good everyday example of a figure that repeats itself when it is turned.
(i) Where is the centre of rotation of the fan?
(ii) Through what smallest angle must the fan be turned so that it looks the same as before?
(iii) What is the order of rotational symmetry of the fan?
(iv) Does the fan seen from below have a line of symmetry? Give a reason.
Answer:
(i) At the middle of the round hub, where the blades are joined to the rod.
(ii) The three blades share a full turn equally: 360° ÷ 3 = 120°.
(iii) The fan looks the same after 120°, 240° and 360°, so the order is 3.
(iv) No. All the blades bend the same way, so in a mirror they would bend the other way. No fold makes the two halves cover each other.
In simple words: Three equal bent blades give order 3 with a smallest turn of 120°, but no line of symmetry.

Teacher's Note:
1. Blades bent one way remove line symmetry.
2. The fan is like a three-blade pinwheel.

Question 13. Imran makes a paper kite
Imran made a kite for Makar Sankranti. He used one long stick from the top corner to the bottom corner and one shorter stick across it. He pasted coloured paper over the sticks, so the kite had four sides, and the half on the left of the long stick was exactly like the half on the right. He drew the same flower design on both halves and tied the same tail at the bottom corner. His sister said the kite would fly straight only if the two halves balanced each other exactly.
(i) Which stick of the kite lies along a line of symmetry?
(ii) How many lines of symmetry does Imran’s kite shape have?
(iii) Does the kite shape have rotational symmetry? Give a reason.
(iv) If both sticks were of the same length and each crossed the other exactly at its middle point, at right angles, which shape would the paper take, and how many lines of symmetry would it then have?
Answer:
(i) The long stick, running from the top corner to the bottom corner.
(ii) Exactly 1 line of symmetry.
(iii) No. Turned about the crossing point of the sticks, the kite looks the same only after a full turn of 360°. No smaller turn works, so it has no rotational symmetry.
(iv) The paper would be a square, which has 4 lines of symmetry (and order of rotational symmetry 4).
In simple words: The kite folds only along its long stick; equal sticks crossing at their middles at right angles give a square with 4 lines.

Teacher's Note:
1. A kite shape has one line of symmetry and no rotational symmetry.
2. Equal diagonals that bisect each other at right angles make a square.

Teacher's Note:
1. Regular polygon: order = number of sides.
2. The circle always wins for lines of symmetry.

Question 15. A paper craft for the festival
Riya is making a paper hanging for a festival. She takes a square sheet of coloured paper and folds it once from left to right. Without opening it, she folds it once more from top to bottom. The folded paper now lies in four layers. She then cuts one small shape out of the folded paper, cutting through all four layers at once, and opens the sheet. Her brother tries the same thing with a long rectangular strip, folding it in half three times before making one cut. Both of them get a pretty pattern with repeated shapes.
(i) How many identical shapes appear on Riya’s sheet when she opens it?
(ii) What do the two fold lines become in the opened sheet?
(iii) Where must Riya cut so that the opened sheet has one square hole exactly in the middle?
(iv) How many identical shapes will her brother get from his strip after folding it in half three times?
Answer:
(i) The cut goes through 4 layers, so 4 identical shapes appear.
(ii) They become lines of symmetry of the opened sheet: one vertical and one horizontal line through the middle.
(iii) At the closed corner where the two folded edges meet, since that corner is the centre of the sheet. A small square cut there, with two sides along the folded edges, opens into one square hole in the middle.
(iv) Three folds in half give 2 × 2 × 2 = 8 layers, so one cut gives 8 identical shapes.
In simple words: Each fold doubles the layers; the folds become lines of symmetry and the closed corner is the centre.

Teacher's Note:
1. Number of shapes = number of layers.
2. Each fold in half doubles the layers.

Question 16. A game of cards and letters
Ananya is playing a card game. She notices that the card showing two hearts (one upright at the top and one upside down at the bottom) looks exactly the same as before when she turns it upside down. Her friend then writes five capital letters on the board for a word game:
A, H, N, S, T
Ananya turns the board upside down and finds that some of the letters still read the same, while others do not. She also stands a small mirror upright on the board and finds that some letters look unchanged in the mirror.
(i) Through what angle has Ananya turned the card so that it looks the same?
(ii) What is the order of rotational symmetry of the card, and what are its angles of symmetry?
(iii) Which of the five letters look exactly the same after the board is turned upside down?
(iv) Which letter in the list has both a line of symmetry and rotational symmetry, and how many lines of symmetry does it have?
Answer:
(i) Through 180°, a half turn.
(ii) The card falls on itself after a half turn and after a full turn, so its order is 2 and its angles of symmetry are 180° and 360°.
(iii) H, N and S. A and T do not, because they end up pointing downwards.
(iv) H. It has rotational symmetry of order 2 and also 2 lines of symmetry, one vertical and one horizontal.
In simple words: The card and H, N, S look the same after a half turn; only H also has lines of symmetry (two).

Teacher's Note:
1. Upside down means a 180° turn.
2. N and S have rotational symmetry but no line of symmetry.

Question 17. A border for the classroom wall
Class 6 painted a long border strip along the classroom wall. The strip is a straight line with identical triangles standing on it, one after another, and every triangle points upwards. The triangles are all of the same size and are equally spaced. Later, Kabir looked at a photograph of the border and turned the photograph upside down. He said that the border no longer looked the way it did before, even though it is made of a pattern that repeats.
(i) Does the border strip have a line of symmetry? Where does it lie?
(ii) Does the strip look the same after a half turn about its centre? Give a reason.
(iii) What is the only angle of symmetry of this border?
(iv) What simple change in the pattern will make the border look the same after a half turn?
Answer:
(i) Yes. A vertical line through the tip of a triangle is a line of symmetry; so is a vertical line through the middle of the gap between two neighbouring triangles.
(ii) No. After a half turn all the triangles point downwards and the straight line comes above them, so the border does not look as before.
(iii) Only 360°, so the border has no rotational symmetry.
(iv) Paint a matching row of identical triangles pointing downwards below the line, one under each upper triangle. Then a half turn about the centre makes the pattern look the same.
In simple words: The border has vertical lines of symmetry but no rotational symmetry until a matching downward row is added.

Teacher's Note:
1. Repeating a pattern is not the same as rotational symmetry.
2. A half turn turns 'up' into 'down'.

Question 18. Designing the school logo
The art club is designing a new logo for the school. The design has a small round centre, and six identical green petals are drawn around it. Each petal is curved, and every petal curves in the same direction, like the blades of a paper pinwheel. The design was made by drawing one petal and then turning it again and again about the centre through the same angle until the ring of petals was complete.
(i) About which point was each new petal turned?
(ii) What is the smallest angle of symmetry of this logo?
(iii) What is its order of rotational symmetry?
(iv) Does the logo have a line of symmetry? Give a reason for your answer.
Answer:
(i) About the small round centre of the design; this point is the centre of rotation.
(ii) Six identical petals share a full turn equally: 360° ÷ 6 = 60°.
(iii) The logo falls on itself after 60°, 120°, 180°, 240°, 300° and 360°, so its order is 6.
(iv) No. All six petals curve the same way; in a mirror they would curve the other way, so no fold makes the halves cover each other. The logo has rotational symmetry but no reflection symmetry, like a pinwheel.
In simple words: Six petals turned about the centre give order 6 and 60°, but their one-way curve removes line symmetry.

Teacher's Note:
1. Count the petals to get the order.
2. One-way curved parts mean no line of symmetry.

Question 19. The new Parliament Building
The new Parliament Building in New Delhi, seen from above, has an outer boundary in the shape of a triangle whose three sides are alike. Pictures taken from a drone show this triangular boundary clearly. For a class project, Nitin printed such a picture, traced its outer boundary on a sheet, cut the tracing out, and turned the cut-out over the printed picture to test it for symmetry. He also folded the tracing in different ways to find out how the two halves matched each other.
(i) Does the outer boundary have reflection symmetry? If yes, how many lines of symmetry does it have?
(ii) What is its order of rotational symmetry and its smallest angle of symmetry?
(iii) After which of these turns will the boundary look exactly the same: 90°, 120°, 180°, 240°?
(iv) Suppose a dome is built at just one corner of the triangle. What happens now to the lines of symmetry and to the rotational symmetry of the shape seen from above?
Answer:
(i) Yes. It has 3 lines of symmetry, each through a corner and the middle of the opposite side.
(ii) Order 3; smallest angle 360° ÷ 3 = 120°.
(iii) After 120° and 240° (and 360°). Turns of 90° and 180° do not bring it back.
(iv) The dome makes one corner different. Only 1 line of symmetry is left, through that corner and the middle of the opposite side. The rotational symmetry is lost, because a 120° turn carries the dome to a corner without a dome; only 360° remains.
In simple words: The equilateral boundary has 3 lines and order 3; a dome at one corner leaves 1 line and no rotational symmetry.

Teacher's Note:
1. Angles of symmetry are multiples of 120° here.
2. Making one part different breaks symmetry.

Question 20. A mehndi design
Zoya is drawing a mehndi design on her sister’s palm. She first draws a small circle at the centre. Around this circle she draws eleven identical petals, placed at equal distances all around, so that the whole design looks the same each time it is turned through a fixed amount. Each petal is itself alike on its two sides. After finishing the drawing, she colours one single petal dark red and leaves the other ten light brown, because her sister wanted one petal to stand out from the rest.
(i) What is the order of rotational symmetry of the design before any petal is coloured differently?
(ii) Find its smallest angle of symmetry. Is it a whole number of degrees? Write it as a mixed fraction if it is not.
(iii) How many lines of symmetry does the design have before the colouring?
(iv) After one petal is coloured dark red, what are the angles of symmetry and the lines of symmetry of the design?
Answer:
(i) The 11 identical petals are equally placed, so each takes the place of the next on turning. Order = 11.
(ii) 360° ÷ 11: since 11 × 32 = 352 and 360 − 352 = 8, the angle is \( 32\frac{8}{11} \)°. It is not a whole number of degrees.
(iii) Each petal is alike on its two sides and they are evenly placed, so there are 11 lines of symmetry, one through each petal and the centre.
(iv) Only 360° remains as an angle of symmetry, so there is no rotational symmetry now. Just 1 line of symmetry survives: the line through the dark red petal and the centre.
In simple words: 11 petals give order 11 and an angle of 32 8/11 degrees; colouring one petal leaves only 1 line and no rotation.

Teacher's Note:
1. Angles of symmetry need not be whole numbers.
2. One odd petal keeps only the line through itself.