Stage 8 - Q1 - 2 marks
How many reflection lines does a regular pentagon have?
Hint
The polygon is regular.
Stage 8 - Q2 - 2 marks
What is the rotational order of a regular octagon?
Hint
Count how many matching positions occur in one turn.
Stage 8 - Q3 - 2 marks
Find the smallest positive rotation of a regular decagon.
Hint
Use the rotational order.
Stage 8 - Q4 - 2 marks
A regular polygon has smallest positive rotation 24°. Find its side count.
Hint
Divide a full turn by the given angle.
Stage 8 - Q5 - 2 marks
State the reflection-line count and rotational order of a non-square rectangle.
Hint
Do not assume a diagonal is a symmetry line.
Stage 8 - Q6 - 2 marks
Give a quadrilateral with no reflection lines but rotational order 2.
Hint
Think about a slanted parallelogram.
Stage 8 - Q7 - 2 marks
A shape matches after a 90° rotation. List two possible rotational orders and explain.
Hint
A stated matching angle need not be the smallest one.
Stage 8 - Q8 - 3 marks
A regular polygon has more than 8 sides and a smallest positive rotation larger than 30°. Find all possible side counts.
Hint
Convert the angle condition into a bound on the side count.
Stage 8 - Q9 - 4 marks
Explain why a non-square rhombus cannot have rotational order 4.
Hint
Ask what a quarter-turn does to its adjacent angles.
Stage 8 - Q10 - 5 marks
Challenge: find all regular polygons whose smallest positive rotation is strictly between 20° and 30°. Prove that your list is complete.
Hint
Larger side counts give smaller rotation angles.