Higher June 2022 Paper 4 Q4
4 Three regular polygons meet at a point.
Not to scale
Two of the polygons are pentagons.
Find the number of sides of the third polygon.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 10 with correct working | 6 | “correct working” requires at least M1M1 or M2 | |
| M2 for a correct method to find the interior angle of a pentagon e.g. \(180 - \frac{360}{5}\) or \(\frac{(5 - 2) \times 180}{5}\) or M1 for partial method e.g. \(\frac{360}{5}\) or \((5 - 2) \times 180\) | M2 implied by 108 M1 implied by 72 or 540 | ||
| AND | |||
| M1 for 360 – 2 × their 108 | M3 implied by 144 | ||
| AND | |||
| M2 for \(\dfrac{360}{180 - \textit{their } 144}\) or M1 for 180 − their 144 | M1 for \((n - 2)180 = \textit{their } 144n\) oe and M1 for a correct rearrangement e.g. \(36n = 360\) Alternative method as the third angle is the sum of the two exteriors of the pentagons M3 for \(2 \times \frac{360}{5}\) [ = 144] or M1 for \(\frac{360}{5}\) and M2 for \(\dfrac{360}{360 - \textit{their } 144 - 180}\) oe or M1 for 360 – their 144 – 180 oe | ||
| If 0, 1 or 2 scored, instead award SC3 for answer 10 with no working or insufficient working | |||