Higher January 2021 Paper 1R Q8
8 The diagram shows a regular pentagon, \(ABCDE\), a regular hexagon, \(CFGHID\), and a quadrilateral, \(EDIJ\).
Diagram NOT accurately drawn
\(AEJ\) and \(HIJ\) are straight lines.
Work out the size of the angle marked \(x\).
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| (5 – 2) × 180 ÷ 5 (= 108) or 360 ÷ 5 (= 72) | M1 |
| (6 – 2) × 180 ÷ 6 (= 120) or 360 ÷ 6 (= 60) | M1 |
| 360 – 108 – 120 (= 132) or 60 + 72 (= 132) or (180 – ‘120’) + (180 – ‘108’) | M1 |
| 360 – ‘72’ – ‘60’ – ‘132’ (= 96) | M1 |
| Working required Answer: 96 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for method to find an interior or exterior angle of a pentagon
M1: for method to find an interior or exterior angle of a hexagon
M1: dep on M2 for a correct method to find angle \(EDI\) using correct figures
M1: for a complete method to find angle \(x\)
A1: dep on correct working
Note: Angles may be seen on diagram throughout