Question 35

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waecmaths question: 

In the diagram GI is a tangent to the circle at H. If $EF\parallel GI$ calculate the size$\angle EHF$

Option A: 

126o

Option B: 

72o

Option C: 

54o

Option D: 

28o

waecmaths solution: 

$\begin{align}  & \angle HFE=\angle FHI={{54}^{\circ }}\text{   }\!\!\{\!\!\text{ Alternate angele }\!\!\}\!\!\text{ } \\ & \angle HEF=\angle HFE={{54}^{\circ }}\text{   }\!\!\{\!\!\text{ opposite segments }\!\!\}\!\!\text{ } \\ & \angle EHF={{180}^{\circ }}-\angle HEF-\angle HFE \\ & \angle EHF={{180}^{\circ }}-{{54}^{\circ }}-{{54}^{\circ }}={{72}^{\circ }} \\\end{align}$

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