4MA0 Foundation June 2013 Paper 2R Q19

19

Pentagon ABCDE with DC parallel to AB and exterior angles 67° at A, 112° at B, x° at C, 74° at D and y° at E

Diagram NOT accurately drawn

The diagram shows a pentagon \(ABCDE\).
\(DC\) is parallel to \(AB\).

The size of an exterior angle at \(A\) is \(67^\circ\)
The size of an exterior angle at \(B\) is \(112^\circ\)
The size of an exterior angle at \(C\) is \(x^\circ\)
The size of an exterior angle at \(D\) is \(74^\circ\)
The size of an exterior angle at \(E\) is \(y^\circ\)

(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)