1MA0 Higher March 2013 Paper 1 Q10
*10
Diagram NOT accurately drawn
\(CDEF\) is a straight line.
\(AB\) is parallel to \(CF\).
\(DE = AE\).
Work out the size of the angle marked \(x\).
You must give reasons for your answer. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Angle \(AED = 38\) alternate angles are equal Angle \(ADE = (180 - 38) \div 2 = 71\) \(x = 180 - 71\) base angles of an isosceles triangle are equal angles in a triangle add up to 180 angles on a straight line sum to 180 OR angle \(AEF = 142\) allied angles/co-interior angles add up to 180 \(ADE = 142 \div 2 = 71\) base angles of an isosceles triangle are equal exterior angle of a triangle is equal to the sum of the interior opposite angles, \(x = 180 - 71\) angles in a straight line add to 180 OR Angle \(AED = 38\) alternate angles are equal for angles \(BAE\) and \(AED\) and \(BAD\) and \(ADC\) (\(x\)) Angle \(DAE = (180 - 38) \div 2 = 71\) base angles of an isosceles triangle are equal angles in a triangle add up to 180 Or Angle \(AED = 38\) alternate angles are equal Angle \(ADE = (180 - 38) \div 2 = 71\) base angles of an isosceles triangle are equal and angles in a triangle sum to 180 \(x = 38 + 71\) alternate angles \(BAD\) and \(ADC\) (\(x\)) are equal | \(x = 109\) | 4 | B1 for angle \(AED = 38\) or \(AEF = 142\) M1 for a complete method to find one of the base angles of the isosceles triangle C2 (dep M1) for \(x = 109\) with complete reasons (C1 (dep M1) for one reason correctly used and stated) |