Intermediate June 2017 Unit 2 Q8
8. ABCDE is a regular pentagon with centre O.
Diagram not drawn to scale
Calculate the size of angle \(x\).
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Angle DOC or exterior angle =) \(\dfrac{360(^\circ)}{5}\) | M1 | Answers/working may be seen on diagram. |
| = 72(°) | A1 | Sight of 72 (even x = 72) gains M1A1. |
| (x =) \(\dfrac{180 - 72}{2}\) | M1 | FT ‘their 72’ (but not 60°). |
| = 54(°) | A1 |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Sum of interior angles =) (5 – 2)×180° or equivalent | M1 | |
| = 540(°) | A1 | FT ‘their interior angle sum’ (≠ 900) |
| (x =) ½ × (540 ÷ 5) | M1 | |
| = 54(°) | A1 |