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In rhombus BEAM, what are the measures of ∠AME and ∠AEM?

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20 ∘ and 20 ∘

40 ∘ and 20 ∘

20 ∘ and 4 0 ∘

None of these.

answer is A.

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Detailed Solution

From the given figure we have,

∠ B A M = 70 °

As we know in a rhombus, diagonals bisect each other at right angles.

∴ ∠ B O M = ∠ B O E = ∠ A O M = ∠ A O E = 90 °

Δ A O M

using angle sum property:

∠ A O M + ∠ A M O + ∠ O A M = 180 ° ⇒ 90 ° + ∠ A M O + 70 ° = 180 ° ⇒ ∠ A M O = 180 ° − 90 ° − 70 ° ⇒ ∠ A M O = 20 °

Since, we know, in rhombus all sides are equal in length.
Therefore,

A M = B M = B E = E A

A M = E A

As we know, equal sides make equal angles.

∴ ∠ A M E = ∠ A E M = 20 °

So,

∠ A M E = 20 °

and

∠ A E M = 20 °

.
Hence, option 1 is correct.

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