In rhombus BEAM, find and . - Vidyadip

Question

In rhombus $BEAM$, find $\angle\text{AME}\ \text{and}\angle\text{AEM}.$

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Answer

Given, $\angle\text{BAM}=60^\circ$
We know that, in rhombus, diagonals bisect each other at right angles. $\angle\text{BOM}=\angle\text{BOE}=\angle\text{AOM}=\angle\text{AOE}=90^\circ$
Now, in $\triangle\text{AOM},$ $\angle\text{AOM}+\angle\text{AMO}+\angle\text{OAM}=180^\circ$ [angle sum property of triangle] $\Rightarrow\ 90^\circ+\angle\text{AMO}+70^\circ=180^\circ$
$\Rightarrow\angle\text{AMO}=180^\circ-90^\circ-70^\circ$
$\Rightarrow\angle\text{AME}=20^\circ$
Also, $\Rightarrow\text{AM}=\text{BM}=\text{EA}=\text{EA}$ In $\triangle\text{AME}$, we have $\text{AM}=\text{EA}$
$\therefore\angle\text{AME}=\angle\text{AEM}=20^\circ$ [equal sides make equal angles]

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