Question

In the given figure, $AC$ and $BC$ are the diagonals of Kite $ABCD$ with $AB=AD$ while $AG$ and $ME$ are the diagonals of rectangle $AEGM$. IF $AD=DG$ and $BG$ is a line segment, then $y$ equals

• A. ${21}^0$
• B. ${48}^0$
• C. ${32}^0$
• D. ${62}^0$

Answer 1

The correct option is A ${21}^0$

In $△ABM$ and $△ADM$

$AB=AD$ (Given)

$\angle AMB=\angle AMD\left[{90}^{\circ }\right]$

$AM=AM$ [Common]

Therefore, $△ABM\cong △ADM$ [By SAS]

Hence, $\angle ABM=\angle ADM$ [By CPCT]

$\angle ADM={42}^{\circ }$

$\angle ADM$ is exterior angle of $△ADG$ and In $△ADG$ $AD=AG$

Therefore $\angle AGD=\angle DAG={21}^o$