Question

If $AB\parallel CD,EF\perp CD$ & $\angle GED={126}^{\circ }$, find $\angle AGE,\angle GEF$ & $\angle FGE$.

Answer 1

Now, $AB\parallel CD$ and $GE$ is transversal,

$\therefore$ $\angle AGE=\angle GED$ [ Alternate angles ]

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

Since $AB$ is a line,

$\Rightarrow$ $\angle AGE+\angle FGE={180}^o$ [ Linear pair ]

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

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

$\therefore$ $\angle FGE={54}^o.$

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

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

$\therefore$ $\angle FGE={36}^o$

$\therefore$ $\angle AGE={126}^o,\angle GEF={360}^o,\angle FGE={54}^o$