Stage 8 - Q1 - 2 marks
How many right angles fit around a point?
Hint
Divide the full turn by one corner angle.
Stage 8 - Q2 - 2 marks
Three angles around a point are 75°, 110° and 95°. Find the missing angle.
Hint
Angles around a point total 360°.
Stage 8 - Q3 - 2 marks
A parallelogram has one angle of 65°. Find the adjacent angle.
Hint
Use the parallel sides.
Stage 8 - Q4 - 2 marks
Show that two 65° angles and two 115° angles fill a full turn.
Hint
This is the corner pattern of a parallelogram tiling.
Stage 8 - Q5 - 3 marks
Explain how two congruent trapezia can form a parallelogram.
Hint
Try a 180° turn, rather than a reflection.
Stage 8 - Q6 - 3 marks
Can three 110° corners fill a full turn? If not, find the angle gap.
Hint
Compare the total with 360°.
Stage 8 - Q7 - 3 marks
A proposed vertex uses angles 72°, 108°, 72° and 108°. Does the angle test pass? Is that alone a full proof of a tiling?
Hint
A vertex can fit while other parts of a patch fail.
Stage 8 - Q8 - 4 marks
Design a tiling patch from a non-square rhombus with angles 70° and 110°. Describe the corners at an interior meeting point.
Hint
A rhombus is a parallelogram, so use two side directions.
Stage 8 - Q9 - 4 marks
An irregular quadrilateral has angles 55°, 85°, 125° and 95°. Explain why using four copies of just its 85° corner leaves a gap, but using one of each angle passes the angle test.
Hint
Compare the two proposed arrangements of corners.
Stage 8 - Q10 - 5 marks
Challenge: explain how half-turn copies of any convex quadrilateral can support a tessellation. Your argument must discuss both matching edges and angles; an angle sum alone is insufficient.
Hint
Use one copy of each corner type around a vertex, while explaining why the edges line up.