Higher November 2021 Paper 2 Q5
5 The diagram shows a regular octagon \(ABCDHIJK\) and a pentagon \(DEFGH\).
Diagram NOT accurately drawn
Angle \(GHD\) = angle \(FGH\).
Work out the size of the angle marked \(x\).
Show your working clearly.
(5)
| Scheme | Marks |
|---|---|
| (5 – 2) × 180 – 112 – 102 – 96 (= 230) oe eg 540 – 112 – 102 – 96 (= 230) or 360 – (180 – 112) – (180 – 102) – (180 – 96) (= 360 – 68 – 78 – 104 = 360 – 230 = 130) oe | M1 |
| \(\dfrac{\text{‘}{540}\text{’} - 112 - 102 - 96}{2}\ (= 115)\) or ‘130’ ÷ 2 (= 65) | M1 |
\(\dfrac{180 \times (8 - 2)}{8}\ (= 135)\) or 180 – (360 ÷ 8) (= 135) or \(\dfrac{360}{8}\ (= 45)\) as exterior angle of octagon | M1 |
| 360 – ‘115’ – ‘135’ or ‘65’ + ‘45’ | M1 |
| Working required Answer: 110 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: dep on previous mark
M1: indep
Withhold the mark for \(\dfrac{360}{8}\ (= 45)\) if shown as an interior angle
A1: dep on M1