4MA0 Higher June 2013 Paper 4R Q6
6
Diagram NOT accurately drawn
The diagram shows a pentagon \(ABCDE\).
\(DC\) is parallel to \(AB\).
The size of an exterior angle at \(A\) is 67°
The size of an exterior angle at \(B\) is 112°
The size of an exterior angle at \(C\) is \(x\)°
The size of an exterior angle at \(D\) is 74°
The size of an exterior angle at \(E\) is \(y\)°
(a)
(i) Work out the value of \(x\).
(ii) Work out the value of \(y\).
(4)(b) Work out the sum of the interior angles of the pentagon \(ABCDE\). (2)
| Scheme | Marks |
|---|---|
| (i) \(\angle ABC = 68^\circ\) or \(\angle BCD = 112^\circ\) | M1 |
| 68 | A1 |
| (ii) 360 − (67 + 112 + “68” + 74) | M1 |
| 39 | A1 |
| (4) |
Notes
M1: May be stated or marked on diagram
A1: cao
A1: ft from their (a)(i)
Award 2 marks if the answer to (ii) is 107 − answer to (i)
| Scheme | Marks |
|---|---|
| (5 − 2) × 180 or 3 × 180 or (2 × 5 − 4) × 90 or 6 × 90 or 360 + 180 or (180−67) + (180−112) + (180−“68”) + (180−74) + (180−“39”) or 113 + 68 + 112 + 106 + 141 | M1 |
| 540 | A1 |
| (2) |
Notes
M1: Condone 1 incorrect interior angle
A1: Cao
SC: Award B1 for answer of 108