Question 1210566
The data does not add up. I cannot draw any parallel lines between those points.
If sides EF and GH are parallel, The measures of arcs FG and HE must be the same.
Maybe EF and EG were both supposed to measure 120 degrees, and 40 degrees was the measure of arc HG instead of being the measure of EG.
AS POSTED:
If a quadrilateral inscribed in a circle is called {{{HGFE}}} 
it means that going around the circle in one direction we find the points {{{H}}}, {{{G}}}, {{{F}}}, and {{{E}}} one right after the other in that order.
That means that going from {{{G}}} towards {{{E}}} we passed through {{{F}}}.
Then {{{GF+FE=GE}}}, or {{{FG+EF=EG}}}, so {{{20^o+EF=$40^o}}} --> {{{EF=40^o-20^o=20^o}}} .
The {{{40^o}}} of arc {{{EG}}} include the {{{20^0}}} of arc {{{FG}}} plus the measure of arc {{{EF}}}.
Then {{{HG+GF+FE+EH=HG+20^o+20^o+120^o=360^0}}} 
So, {{{HG+160^o=360^o}}} --> {{{HG=360^o-160^o=200^o}}}
{{{drawing(300,300,-1.2,1.2,-1.2,1.2,
circle(0,0,1),circle(0.985,0.174,0.02),circle(-0.985,0.174,0.02),
circle(0.866,0.5,0.02),circle(0.643,0.766,0.02),
locate(1,0.21,G),locate(-1.1,0.21,H)
,locate(0.9,0.55,F),locate(0.7,0.81,E),
circle (0,0,0.02), locate(0.04,0.05, circle),locate(0.04,-0.06,center)
)}}},