Question

Question 148
In rhombus BEAM, find $\angle AME$ and $\angle AEM$.

Answer 1

Given, $\angle BAM={70}^{\circ }$.
We know that, in rhombus, diagonals bisect each other at right angles.
$\therefore \angle BOM=\angle BOE=\angle AOM=\angle AOE={90}^{\circ }$.
Now, in $\Delta AOM$.
$\angle AOM+\angle AMO+\angle OAM={180}^{\circ }$ . [angle sum property of triangle]
$\Rightarrow {90}^{\circ }+\angle AMO+{70}^{\circ }={180}^{\circ }\Rightarrow \angle AMO={180}^{\circ }-{90}^{\circ }-{70}^{\circ }\Rightarrow \angle AMO={20}^{\circ }$
Also, AM = BM = BE = EA.
In $\Delta AME$, we have,
AM = EA
$\therefore \angle AME=\angle AEM={20}^{\circ }$ [$\because$ equal sides make equal angles]