Question

Question 3
In the given figure, If $AB||CD,EF\perp CD$ and $\angle GED={126}^{\circ },$ find $\angle AGE,\angle GEFand\angle FGE.$

Answer 1

It is given that,
$AB||CD$
$EF\perp CD$
$\angle GED={126}^{\circ }$
$\therefore \angle GEF+\angle FED={126}^{\circ }$
i.e. $\angle GEF+{90}^{\circ }={126}^{\circ }$
$\therefore \angle GEF=126-90={36}^{\circ }$
$\angle AGEand\angle GED$ are alternate interior angles.
$\therefore \angle AGE=\angle GED={126}^{\circ }$
However, $\angle AGE+\angle FGE={180}^{\circ }$ (Linear pair)
i.e. ${126}^{\circ }+\angle FGE={180}^{\circ }$
$\therefore \angle FGE={180}^{\circ }-{126}^{\circ }={54}^{\circ }$
$\therefore \angle AGE={126}^{\circ },\angle GEF={36}^{\circ },\angle FGE={54}^{\circ }$.