Question

In given fig. if $AB||CD,EF\perp CD$ and $\angle GED={126}^o$, find $\angle AGE,\angle GEF$ and $\angle FGE$.

Answer 1

Given,

$AB\parallel CD$, $EF\perp CD$, $\angle GED={126}^{\circ }$

According to the question,

$\angle FED={90}^{\circ }$$(EF\perp CD)$

Now,

$\angle AGE=\angle GED$ (Since, $AB\parallel CD$ and $GE$ is transversal. Alternate interior angles.)

$\therefore \angle AGE={126}^{\circ }$

Also,

$\angle GEF=\angle GED-\angle FED$

$\Rightarrow \angle GEF={126}^{\circ }-{90}^{\circ }$

$\Rightarrow \angle GEF={36}^{\circ }$

Now,

$\angle FGE+\angle AGE={180}^{\circ }$ (Linear pair)

$\Rightarrow \angle FGE={180}^{\circ }-{126}^{\circ }$

$\Rightarrow \angle FGE={54}^{\circ }$