WAEC Mathematics 2010 Paper

Concept:Use the tangent-chord theorem and alternate angles formed by parallel lines $EF$ and $GI$.Explanation:From the diagram, $\angle HFE = 54^\circ$.Since $EF \parallel GI$, alternate interior angles give:$$\angle IHF = \angle HFE = 54^\circ.$$Using the tangent-chord theorem at $H$, the angle between the tangent $GH$ and chord $HE$ equals the angle in the alternate segment:$$\angle GHE = \angle HFE = 54^\circ.$$On the straight line $GHI$, the angles at $H$ add up to $180^\circ$:$$\angle GHE + \angle EHF + \angle IHF = 180^\circ.$$Substitute the known angles:$$54^\circ + \angle EHF + 54^\circ = 180^\circ.$$So,$$\angle EHF = 180^\circ - 108^\circ = 72^\circ.$$Answer:$\angle EHF = 72^\circ$.Correct option: B.