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Question
In rhombus BEAM, find ∠AME and ∠AEM.
Solution
Given, ∠BAM = 70°
We know that, in rhombus, diagonals bisect each other at right angles.
∴ ∠BOM = ∠BOE = ∠AOM = ∠AOE = 90°
Now, In ΔAOM,
∠AOM + ∠AMO + ∠OAM = 180° ...[Angle sum property of triangle]
⇒ 90° + ∠AMO + 70° = 180°
⇒ ∠AMO = 180° – 90° – 70°
⇒ ∠AMO = 20°
Also, AM = BM = BE = EA
In ΔAME, we have,
AM = EA
∴ ∠AME = ∠AEM = 20° ...[∵ Equal sides make equal angles]
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