2025 AHS PRELIMS P1 Q20

In the diagram below, the points \(A\), \(E\), \(C\), \(G\) and \(F\) lie on the circle with centre \(O\). \(BCD\) is a tangent to the circle at \(C\), \(AC\) is the diameter, \(\angle GEF=40^\circ\), \(\angle EGF=58^\circ\) and \(\angle DCG=20^\circ\).

Find, stating your reasons clearly,

1. angle \(ACG\),[1]
2. angle \(AEX\),[1]
3. angle \(FOA\),[1]
4. angle \(GCE\).[2]