In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG and FH are chords. If < FHG = 424∘ ∘ and < EFH = 34∘

In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG and FH are chords. If < FHG = 424${}^{\circ }$ and < EFH = 34${}^{\circ }$

Answer Details

< EFH = < EGH = 34${}^{\circ }$ (angles n the same segment)

< GHF = < GEF = 42${}^{\circ }$(angles in the same segment)

< FOG = 42 + 34 = 76(exterior angle)

< FOG = < EOH = 76(vertically opposite angle)

< EDO = 90${}^{\circ }$, < DOE = $\frac{76}{2}$ = 38${}^{\circ }$

< HEG = 90${}^{\circ }$ - 38${}^{\circ }$ = 52${}^{\circ }$