Higher January 2020 Paper 2R Q12
12 The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y.
Diagram NOT accurately drawn
The two regular polygons each have \(n\) sides.
Work out the value of \(n\).
(3)
| Scheme | Marks |
|---|---|
| 180 – 2 × 66 (= 48) (360 – “48”) ÷ 2 (= 156) 180 – “156” (= 24) | M1 |
| 360 ÷ “24” | M1ft |
| 15 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: Could be marked on diagram
M1ft: Final stage of calculation
Alternative method
| Scheme | Marks |
|---|---|
| 180 – 2 × 66 (= 48) | M1 |
| 360 ÷ (0.5 × “48”) | M1ft |
| 15 | A1 |
Notes
M1: Could be marked on diagram
M1ft: Final stage of calculation
Alternative method
| Scheme | Marks |
|---|---|
180 – 2 × 66 (= 48) (360 – “48”) ÷ 2 (= 156) \(\dfrac{180(n - 2)}{n} = \text{“}156\text{”}\) | M1 |
| \(\text{“}24\text{”}n = 360\) or \(\dfrac{180(15 - 2)}{15}\) (= 156) | M1ft |
| 15 | A1 |
Notes
M1: Could be marked on diagram
M1ft: Final stage of calculation or embedded correct answer.