Mathematics
JAMB 1999
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
-
A.
34o
-
B.
42o
-
C.
52o
-
D.
76o
Correct Answer: Option C
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
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