In the figure,if AB parallel CD,EF perp CD an | vedclass

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(N/A) Given that $AB \parallel CD$,$EF \perp CD$,and $\angle GED = 126^o$.$1$. Since $AB \parallel CD$ and $GE$ is a transversal,the alternate interio

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(N/A) Given that $AB \parallel CD$,$EF \perp CD$,and $\angle GED = 126^o$.
$1$. Since $AB \parallel CD$ and $GE$ is a transversal,the alternate interior angles are equal.
Therefore,$\angle AGE = \angle GED$.
Given $\angle GED = 126^o$,so $\angle AGE = 126^o$.
$2$. We know that $\angle GED = \angle GEF + \angle FED$.
Since $EF \perp CD$,$\angle FED = 90^o$.
Therefore,$126^o = \angle GEF + 90^o$.
$\angle GEF = 126^o - 90^o = 36^o$.
$3$. Since $AB \parallel CD$ and $GE$ is a transversal,the sum of interior angles on the same side of the transversal is $180^o$.
Therefore,$\angle FGE + \angle GED = 180^o$.
$\angle FGE + 126^o = 180^o$.
$\angle FGE = 180^o - 126^o = 54^o$.
Thus,$\angle AGE = 126^o$,$\angle GEF = 36^o$,and $\angle FGE = 54^o$.

In the figure,if $AB \parallel CD$,$EF \perp CD$ and $\angle GED = 126^o$,find $\angle AGE$,$\angle GEF$ and $\angle FGE$.

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