In Fig $\displaystyle AB\ \parallel \ CD$ , and $EF \perp CD$ , $\angle GED = 120°$. Find $\angle GEC , \angle EGF , \angle GEF$
"
Given :
$AB \parallel CD$ and $EF$ is perpendicular to $CD$.
$\angle GED = 120^o$.
To find :
We have to find $\angle GEC, \angle EGF, \angle GEF$
Solution :
$\angle GEF + \ angle CEG = 120^o$
$120^o = \angle GEF + 90^o$
$\angle GEF = 120^o-90^o$
$\angle GEF = 30^o$
$CD$ is a straight line.
Therefore,
$\angle GED + \angle CEG = 180^o$
$120^o+\angle CEG = 180^o$
$\angle CEG = 180^o-120^o$
$\angle GEC = 60^o$
In Triangle $GFE$,
$\angle GFE + \angle GEF+ \angle EGF= 180^o$
$90^o+30^o+\angle EGF= 180^o$
$\angle EGF= 180^o-120^o$
$\angle EGF= 60^o$.
$\angle GEF = 30^o$ , $\angle GEC = 60^o$
$\angle EGF= 60^o$.
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