1MA0 Higher November 2014 Paper 1 Q17
17
Diagram NOT accurately drawn
\(ABCDEFGH\) is a regular octagon.
\(BCKFGJ\) is a hexagon.
\(JK\) is a line of symmetry of the hexagon.
Angle \(BJG\) = angle \(CKF = 140^\circ\)
Work out the size of angle \(KFE\).
You must show all your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| 25 | 4 | M1 for complete method to work out interior angle of a regular octagon or \(135^\circ\) identified as an interior angle of the octagon M1 for complete method to work out angle \(KFG\) or angle \(KFG\) identified as \(110^\circ\) M1 (dep on M2) for complete method to work out angle \(KFE\), eg \(\text{``}135\text{''} - \text{``}110\text{''}\) or \((8 \times \text{``}135\text{''} - 4 \times \text{``}135\text{''} - 4 \times \text{``}110\text{''}) \div 4\) or \((3 \times 180 - 2 \times \text{``}135\text{''} - 2 \times \text{``}110\text{''}) \div 2\) A1 for 25 with supporting working OR M1 for complete method to work out the exterior angle of a regular octagon or \(45^\circ\) identified as an exterior angle of the octagon M1 for complete method to work out angle \(KFG\) or angle \(KFG\) identified as \(110^\circ\) M1 (dep on M2) for complete method to work out angle \(KFE\), eg \(180 - \text{``}45\text{''} - \text{``}110\text{''}\) A1 for 25 with supporting working OR M1 for complete method to work out the exterior angle of a regular octagon or \(45^\circ\) identified as an exterior angle of the octagon M1 for complete method to work out angle \(JKF\) or angle \(JKF\) identified as \(70^\circ\) M1 (dep on M2) for complete method to work out angle \(KFE\), eg \(\text{``}70\text{''} - \text{``}45\text{''}\) A1 for 25 with supporting working |