Higher June 2017 Paper 3 Q5
5 In the diagram, \(AB\), \(BC\) and \(CD\) are three sides of a regular polygon P.
Show that polygon P is a hexagon.
You must show your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| Shows polygon is a hexagon | M1 | for a complete method to find the interior or exterior angle of the dodecagon eg \(180 - \dfrac{360}{12}\), \(\dfrac{180}{12}(12 - 2)\) oe \((= 150)\), \(360 \div 12\ (=30)\) |
| M1 | for a complete method to find the interior angle of polygon P eg at \(B\) or \(C\): \(360 - \text{``}150\text{''} - 90\ (= 120)\) or \(\text{``}30\text{''} + 90\ (= 120)\) or for a complete method to find the interior or exterior angle of the hexagon eg \(180 - \dfrac{360}{6}\), \(\dfrac{180}{6}(6 - 2)\) oe \((= 120)\), \(360 \div 6\ (= 60)\) | |
| A1 | for 30 and 120 or 30 and 60 or 120 and 150 or 60 and 150 | |
| C1 | complete solution, fully supported by accurate figures |