1MA0 Higher June 2016 Paper 2 Q12
12
Diagram NOT accurately drawn
The diagram shows a regular pentagon.
\(AB\) and \(CD\) are two of the lines of symmetry of the pentagon.
Work out the size of the angle marked \(x\).
You must show all your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| 144 | 4 | M1 for method to find the interior angle of a regular pentagon, eg. \(180 \times (5 - 2) \div 5\) (= 108) oe M1 (indep) for using a line of symmetry to find an angle, eg. “interior angle” \(\div\) 2 (half an interior angle) or 90 between line and side M1 (dep on M2) for complete method to find angle \(x\), eg. \(90 + \text{``}54\text{''}\) or \(\text{``}108\text{''} \times 5 - \text{``}108\text{''} \times 2 - 90 \times 2\) A1 for 144 supported by working OR M1 for considering all 5 lines of symmetry or angle vertically opposite \(x\) with angle bisector drawn M1 for \(360 \div 10\) (= 36) or \(360 \div 5\) (= 72) M1 for \((360 \div 10) \times 4\) or \((360 \div 5) \times 2\) A1 for 144 supported by working OR M1 for method to find the exterior angle of a regular pentagon (72°), eg. \(360 \div 5\) (= 72) oe M1 (indep) for using a line of symmetry to find an angle, eg. “interior angle” \(\div\) 2 (half an interior angle) or 90 between line and side M1 (dep on M2) for complete method to find angle \(x\), eg. \(180 - 2(180 - 90 - 72)\) A1 for 144 supported by working |