Higher June 2023 Paper 5 Q10
10 A student draws two different regular polygons.
The exterior angle of one polygon is \(p\)°.
The exterior angle of the other polygon is \(q\)°.
The sum of \(p\) and \(q\) is 112°.
The difference between \(p\) and \(q\) is 32°.
Find the number of sides of each polygon.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5 and 9 with correct working | 6 | M3 for 72 and 40 OR M2 for 72 or 40 OR B1 for \(p + q = 112\) oe B1 for \(p - q = 32\) or \(q - p = 32\) oe AND M1 for 360 ÷ their p or 360 ÷ their q oe or \(\frac{180(n - 2)}{n}\) = 180 – their p or \(\frac{180(n - 2)}{n}\) = 180 – their q oe A1 for one correct answer If 0 or 1 scored, instead award SC2 for both answers correct with no or insufficient working If 0 scored award SC1 for one correct answer with no or insufficient working | “Correct working” requires evidence of M3 and M1 \(2p = 112 + 32\) oe implies B1B1 \(2q = 112 - 32\) oe implies B1B1 M1 could be repeated addition oe For M1, accept e.g. 360 ÷ 5 = 72 or other convincing justification A1dep on at least M2 and M1 leading to that answer |