In the diagram above, EFGH is a cyclic quadrilateral in which EH//FG, EG and FH…

Mathematics JAMB 1999

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

  • 34o
  • 42o
  • 52o checkmark
  • 76o

The correct answer is: C

Explanation

∠EFH = ∠EGH(∠s in same segment)
= 34o
∠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 = 52o
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