Higher June 2018 Paper 3 Q8
8 \(ABCDE\) is a pentagon.
Angle \(BCD = 2 \times\) angle \(ABC\)
Work out the size of angle \(BCD\).
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 140 | P1 | for complete process to find sum of the interior angles of a pentagon eg \((5 - 2) \times 180\) or exterior \(360 \div 5 = 72\), interior \(180 - 72 = 108\), \(108 \times 5\) OR for complete process to find sum of the exterior angles of the pentagon eg \((180 - x) + (180 - 2x) + (180 - 125) + (180 - 115) + (180 - 90)\) |
| A1 | for sum of interior angles is 540 OR for sum of exterior angles is 360 | |
| P1 | for start to process to find angle \(ABC\) eg [angles in a pentagon] \(-\ 115 - 125 - 90\ (= 210)\) or \(115 + 125 + 90 + x + 2x =\) [angles in a pentagon] OR \((180 - x) + (180 - 2x) + (180 - 125) + (180 - 115) + (180 - 90) = 360\) | |
| P1 | for process to find angle \(ABC\) eg \(\text{``}210\text{''} \div 3\ (= 70)\), “210” divided in the ratio 2 : 1 or for process to find angle \(BCD\) eg \(\dfrac{2}{3} \times \text{``}210\text{''}\) or for \(3x = \text{``}210\text{''}\) or \(-3x = -\text{``}210\text{''}\) | |
| A1 | cao |
Additional guidance
Must be a complete process that could lead to a figure of 540 if that process is evaluated incorrectly
360 must be identified as the sum of the exterior angles
Award provided [angles in a pentagon] is greater than 400
Algebraic route needs to show both sides of the equation.
LHS of equation may be simplified
Award if 70 is given for either \(ABC\) or \(BCD\) on the diagram
Award marks for 140 on the diagram with working and not contradicted by the answer line.
Award 0 marks for 140 without working.