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

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

Answer Details

∠EFH = ∠EGH(∠s in same segment)
= 34${}^{\circ }$
∠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${}^{\circ }$