Question

In figure, line DE $||$ line GF ray EG and ray FG are bisectors of $\angle$DEF and $\angle$DFM respectively. then $\angle$DEG$=\frac{1}{2}\angle$EDF.

• A. True
• B. False

Answer 1

The correct option is A True

$DE||GF$

Let $\angle GEF=x$

then

$\angle GEF=\angle DEG=x$ [EG angle bisector]

as $DE||GF$

so, $\angle DEF=\angle GFM=2x$ [corresponding angle]

$\angle GFM=\angle DFG=2x$ [FG angle bisector]

$\angle MFD=\angle E+\angle D$ [exterior angle property]

$\angle D=4x-2x$

$\angle D=2x$

$\angle DEG=x$

$\angle EDF=2x$

$\angle DEG=\frac{1}{2}\angle EDF$