(a) The diagram below shows some tiles in part of a tessellation. The tiles are all identical regular hexagons. Each of the interior angles is 120°.
Explain why the tiles tessellate. You must give a reason, based on angle facts, for your answer. [1]
(b) Explain why tiles that are identical regular pentagons will not tessellate. You must show working to support your explanation. [4]
Mark scheme (a)
Scheme
Marks
Comments
Valid explanation which refers to use of angles at a point 360° e.g. “three (interior) angles can be added together to make 360°” “120 is a factor of 360” “360 is a multiple of 120” “360 ÷ 3 = 120” or equivalent “120 × 3 = 360” or equivalent
E1
Do not accept “they fit together” “they all add up to 360” (unless ‘they’ are identified as the three (interior) angles – could be on diagram) “all exterior angles add up to 360”
May be seen in stages. Award M1 for any one of the following:
(Exterior angle =) 360 ÷ 5
(Exterior angle =) 72
(Sum of the interior angles =) (5 – 2) × 180
(Sum of the interior angles =) 540.
108(°)
A1
CAO.
Valid explanation which refers to 108(°) AND 360 (°) e.g. “108 is not a factor of 360” “360 is not a multiple of 108” “360 ÷ 108 is not a whole number” or equivalent.
E1
Dependent on M2 previously awarded. FT ‘their 108’.
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