In a rhombus, the diagonals bisect each other and also bisect the angles of the rhombus. Since you are given \( m\angle A = 114^\circ \), we can find \( m\angle B \).
In a rhombus, opposite angles are equal, and the adjacent angles are supplementary (they add up to \( 180^\circ \)). Therefore:
\[ m\angle A + m\angle B = 180^\circ \]
Substituting the known value of \( m\angle A \):
\[ 114^\circ + m\angle B = 180^\circ \]
To find \( m\angle B \), we can rearrange the equation:
\[ m\angle B = 180^\circ - 114^\circ = 66^\circ \]
Thus, \( m\angle B = 66^\circ \).
The correct answer is \( \boxed{66} \).
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