Higher November 2021 Paper 6 Q10
10 An equilateral triangle, a regular 10-sided polygon and another regular polygon meet at a point.
Not to scale
(a) Show that angle A is 156°. [3]
(b) Work out the number of sides of the other regular polygon. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Using interior angles ((10 – 2) × 180) ÷ 10 or 1440 ÷ 10 seen | 1 | Using exterior angles 360 ÷ 10 seen | Mark the working Mark angles on the diagram only if 0 scored |
| [Int angle of triangle =] 60 in working | 1 | [Ext angle of triangle =] 120 in working | |
| 360 – (144 + 60) oe [= 156] | 1 | 36 + 120 [= 156] | |
| Alternative method 360 ÷ 10 seen | 1 | ||
| [Int angle of triangle =] 60 in working | 1 | ||
| 180 – (60 – 36) [= 156] | 1 | If 0 scored SC1 for 24, 36, 60, 120 or 144 shown in the correct place on the diagram | Working backwards from 156 to 144 [to 10 sides] scores 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 15 | 2 | M1 for [\(n =\)] \(\dfrac{360}{180 - 156}\) or \(\dfrac{180(n - 2)}{n} = 156\) | |