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
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Correct Answer: Option 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
∠ 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