JAMB Mathematics 2018 Paper

Concept:Use parallel-line angle properties and the tangent-chord theorem to find the required angle.Explanation:Since $EF \parallel GI$, the alternate angle $\angle IHF$ equals $\angle EFH$.From the diagram, $\angle EFH = 54^{\circ}$, so $\angle IHF = 54^{\circ}$.By the tangent-chord theorem, the angle between tangent $GH$ and chord $HE$ equals the angle in the alternate segment:$\angle EHG = \angle EFH = 54^{\circ}$.Since $GHI$ is a straight line, the angles on the same side of the tangent at $H$ sum to $180^{\circ}$:$\angle IHF + \angle EHF + \angle EHG = 180^{\circ}$.Substitute the known angles:$54^{\circ} + \angle EHF + 54^{\circ} = 180^{\circ}$.$\angle EHF = 180^{\circ} - 108^{\circ} = 72^{\circ}$.Answer:$\angle EHF = 72^{\circ}$. Therefore, the correct option is B.