# 3.  In Fig. 6.30, if AB $||$ CD, EF $\bot$ CD and $\angle$ GED = 126°, find $\angle$ AGE, $\angle$ GEF and $\angle$ FGE.

Given AB || CD, EF$\perp$CD and $\angle$GED = $126^0$
In the above figure,
GE is transversal. So, that $\angle$AGE = $\angle$GED =  $126^0$ [Alternate interior angles]
Also, $\angle$GEF = $\angle$GED - $\angle$FED
= $126^0-90^0 = 36^0$
$\angle GEF = 36^0$

Since AB is a straight line
Therefore, $\angle$AGE  + $\angle$FGE =  $180^0$
So, $\angle$FGE = $180^0-\angle AGE = 180^0 - 126^0$
$\Rightarrow \angle FGE =54^0$

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