In rhombus BEAM, find ∠AME and ∠AEM.

Question

In rhombus BEAM, find

∠ A M E

and

∠ A E M

Answer:
:
Given,

∠ B A M = 70^{\circ}

.
We know that, in rhombus, diagonals bisect each other at right angles.

∴ ∠ B O M = ∠ B O E = ∠ A O M = ∠ A O E = 90^{\circ}

.
Now, in

Δ A O M

∠ A O M + ∠ A M O + ∠ O A M = 180^{\circ}

. [angle sum property of triangle]

\Rightarrow 90^{\circ} + ∠ A M O + 70^{\circ} = 180^{\circ} \Rightarrow ∠ A M O = 180^{\circ} - 90^{\circ} - 70^{\circ} \Rightarrow ∠ A M O = 20^{\circ}

Also, AM = BM = BE = EA.
In

Δ A M E

, we have,
AM = EA

∴ ∠ A M E = ∠ A E M = 20^{\circ}

[

∵

equal sides make equal angles]

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