解:根据题意,得$∠AED+∠DEF = 180°,$
$∠FGC+∠BGF = 180°。$
$ $因为$∠DEF = 120°,$$∠FGC = 118°,$
所以$∠AED = 180°-∠DEF = 180°-120°=60°,$
$∠BGF = 180°-∠FGC = 180°-118°=62°。$
$ $因为$DE// CG,$$FG// CD,$
所以$∠B=∠AED = 60°,$$∠C=∠BGF = 62°。$
$ $因为$\triangle ABC$的内角和为$180°,$
所以$∠A = 180°-∠B-∠C = 180°-60°-62°=58°$