Question

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

Answer 1

Given $AB\parallel CD$ and $\angle GED={120}^o,\angle FED={90}^o$

$\angle GED=\angle AGE$ [alternate interior angles ]

Now,

since AB is a line,

$\angle AGE+\angle FGE=180$

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

$\angle FGE={54}^o$

Now,

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

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

$\angle GEF={36}^o$