Question

In Fig., if $AB\parallel CD$ and $\angle GED=126$, find $\angle AGE,\angle GEF$ & $\angle FGE$.

Answer 1

$AB\parallel CD$ and $GE$ is the transversal.

Hence, $\angle AGE=\angle GED$ (alternate angles)

$\Rightarrow \angle AGE={126}^0$

Now, since $AB$ is a line

$\angle AGE+\angle FGE={180}^0$(a linear pair)

$\Rightarrow {126}^0+\angle FGE={180}^0$

$\therefore \angle FGE={180}^0-{126}^0={54}^0$

Now,$\angle GEF=\angle GED-\angle EFD$

$\angle GEF={126}^0-{90}^0={36}^0$