Question
In teh diagram, rhombus ABCD has a diagonal line DB, and m<A=114. WHat is m<B of rhombus ABCD?
66
33
57
114
66
33
57
114
Answers
GPT-4o mini
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 \( \boxed{66} \).
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 \( \boxed{66} \).