Intermediate June 2019 Unit 1 Q12
12. A regular octagon with centre O is shown below.
Diagram not drawn to scale
Calculate the exact size of \(O\hat{A}B\).
You may choose to draw additional lines on the diagram to help you.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Angle AÔB or exterior angle =) \(\dfrac{360}{8}\)(°) | M1 | Answers/working may be seen on diagram. |
| = 45(°) | A1 | Sight of 45 (even e.g. OÂB = 45) gains M1A1. |
| (OÂB =) \(\dfrac{180 - 45}{2}\) | M1 | FT ‘their 45’ (but not 60°). |
| = 67·5(°) | A1 |
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| (Sum of interior angles =) (8 – 2)×180° or equivalent | M1 | |
| = 1080(°) | A1 | (Interior angle =) 135(°) implies M1A1 |
| (OÂB =) ½ × (1080 ÷ 8) or equivalent | M1 | FT ‘their interior angle sum’ (≠ 1440) |
| = 67·5(°) | A1 |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| (Using 16 right-angled triangles.) (Angle at O =) 360 / 16 | M1 | |
| = 22·5(°) | A1 | |
| (OÂB =) 180 – 90 − 22·5 | M1 | FT ‘their 22·5’. |
| = 67·5(°) | A1 |
(The alternative methods are printed in italics in the original.)