Question

Circle D has diameter EF. The measure of ∠GDF = 55° What is the measure of EH?
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Answer 1

the complete question in the attached figure

we know that    

if ∠GDF = 55° 

then 
∠EDH is also 55° 

because
ED=DF=radius of a circle
GD=DH=radius of a circle
EH=GF

hence
if  ∠EDH=  55° ( central angle)
then 
arc EH is also  55°

the answer is
arc EH is 55°