Question

In the diagram, rhombus ABCD has a diagonal line DB, and m∠A = 114°. What is m/B of rhombus ABCD?
(1 point)
114°
57°
33°
66°

Answer 1

In a rhombus, opposite angles are equal, and the diagonals bisect each other at right angles. Given that \( m\angle A = 114^\circ \), we know that:

- \( m\angle C = m\angle A = 114^\circ \) (because opposite angles of a rhombus are equal).

The sum of the angles in any quadrilateral is \( 360^\circ \). Therefore, we can find \( m\angle B \) and \( m\angle D \) using the fact that:

\[
m\angle A + m\angle B + m\angle C + m\angle D = 360^\circ
\]
Substituting the known values:

\[
114^\circ + m\angle B + 114^\circ + m\angle D = 360^\circ
\]

This simplifies to:

\[
228^\circ + m\angle B + m\angle D = 360^\circ
\]

Since \( m\angle B = m\angle D \) (opposite angles are equal), we can let \( m\angle B = x \):

\[
228^\circ + x + x = 360^\circ
\]
\[
228^\circ + 2x = 360^\circ
\]
\[
2x = 360^\circ - 228^\circ
\]
\[
2x = 132^\circ
\]
\[
x = 66^\circ
\]

Thus, \( m\angle B = 66^\circ \).

The answer is \( \boxed{66^\circ} \).