JAMB - Mathematics (1999 - No. 34)

In the diagram above, EFGH is a cyclic quadrilateral in which EH//FG, EG and FH are chords. If ∠FHG = 42^o and ∠EFH = 34^o, calculate ∠HEG

34^o

42^o

52^o

76^o

Explanation

∠EFH = ∠EGH(∠s in same segment)
= 34^o
∠HEG = ∠HFG(∠s in same segment)
= X
also ∠HFG = ∠EHF (alternate ∠s)
But ∠EHG + ∠EFG =180(opp sof a cyclic quad)
42 + x + 34 + x = 180
2x + 76 = 180
2x = 180 - 76
2x = 104
x = 52^o

JAMB - Mathematics (1999 - No. 34)

Explanation

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