Question

In the given figure, what is the measure of $\angle FED$?

• A. ${123}^o$
• B. ${154}^o$
• C. ${139}^o$
• D. ${85}^o$

Answer 1

The correct option is C ${139}^o$

$ABCDE$ being a regular pentagon,
$\angle A+\angle B+\angle C+\angle CDE+\angle DEA={540}^o$
$\Rightarrow$ $2y+4y+7^o+{108}^o+5y+6y={540}^o$
$\Rightarrow$ $17y+{115}^o={540}^o$
$\Rightarrow$ $17y={540}^o-{115}^o={425}^o$
$\Rightarrow$ $y={25}^o$
$\therefore$ $\angle CDE=5\times {25}^o=1256o$
$\Rightarrow$ $\angle EDG={180}^o-{125}^o={55}^o$
In quad $FEDG$,
$\angle FED={360}^o-(\angle EFG+\angle FGD+\angle EDG)$
$={360}^o-({76}^o+{90}^o+{55}^o)$
$={360}^o-{221}^o={139}^o$