2025 CHS PRELIMS P2 Q3

\(O\) is the centre of the circle \(ABCDE\). \(XY\) is a tangent to the circle at \(E\) and \(EC\) intersects \(BD\) at \(F\). \(OZ\) is a straight line that passes through \(A\) and is parallel to \(XY\). The lines \(CB\) produced and \(EA\) produced meet at \(W\). \(\angle BCE=71^\circ\) and \(\angle OBC=64^\circ\).

1. Complete the following statements.
   1. \(\angle BDE=\ldots^\circ\) because …[2]
   2. \(\angle AOE=\ldots^\circ\) because …[2]
2. Find \(\angle BOE\).[1]
3. Find \(\angle OCE\).[1]
4. Find \(\angle ABW\).[2]