Higher June 2017 Paper 5 Q8
8 Imran joins two tiles together as shown below.
One tile is a regular hexagon and the other tile is a regular pentagon.
Not to scale
(a) Show that angle \(a\) is 132°. [3]
(b) Imran thinks that another tile in the shape of a regular polygon will fit exactly into angle \(a\).
Is Imran correct?
Show your reasoning. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 360 ÷ 5 and 360 ÷ 6 | M1 | or for ((5 – 2) × 180) ÷ 5 oe and ((6 – 2) × 180) ÷ 6 oe | M1 allow 540 ÷ 5 and 720 ÷ 6 but not for just 108 and 120 Allow recovery of missing brackets from answers nfww for B1 do not allow if e.g. 60 is shown as int angle of hexagon |
| [Ext angle = ] 72 or 60 seen | B1 | or [Int angle =] 120 or 108 seen | |
| 60 + 72 [= 132] or 360 – (108 + 120) [=132] | A1 | with no errors seen | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [ext angle =] 180 – 132 oe or \(\frac{180(n - 2)}{n}\) = 132 oe | M1 | Or [Int angle = ] ((7 – 2) × 180) ÷ 7 oe | M1 implied by 48 or 128 to 129 |
| 360 ÷ (180 – 132) oe soi Or for 360 ÷ 8 oe and 360 ÷ 7 oe Or for 48 × 7 and 48 × 8 | M1 | Or [Int angle =] ((8 – 2) × 180) ÷ 8 oe | M1 implied by 135 Division can be implied from a correct conclusion e.g. 360 is not a multiple of 48 gets M1A1 M1 Implied by 45 and 51 to 52 |
| No and correct conclusion | A1 | e.g. explains that 360 ÷ 48 gives non - integer answer or 128 is 7 sided polygon and 135 is 8 sided polygon so No | |