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Question

A parallelogram's top left vertex is given as upper A, its top right vertex is given as upper B, its bottom left vertex is given as upper D, and its bottom right vertex is given as upper C. A diagonal line connects upper B and upper D.

In the diagram, rhombus ABCD has a diagonal line DB¯¯¯¯¯¯¯¯, and m∠A=114°. What is m∠B of rhombus ABCD?

(1 point)
Responses use your mental math

114°
114°

57°
57°

66°
66°

33°
33°
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Answer 1

In a rhombus, opposite angles are equal, and the sum of the angles in any quadrilateral is \(360^\circ\). Given that \(m\angle A = 114^\circ\), we can find \(m\angle B\).

Since \(m\angle A\) is \(114^\circ\), angle \(C\) (which is opposite angle \(A\)) is also \(114^\circ\).

Now, the sum of angles \(A\), \(B\), \(C\), and \(D\) must equal \(360^\circ\):

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

Using the fact that \(m\angle C = m\angle A = 114^\circ\) and \(m\angle D = m\angle B\), we can express the equation as:

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

This simplifies to:

\[ 228^\circ + 2m\angle B = 360^\circ \]

Subtract \(228^\circ\) from both sides:

\[ 2m\angle B = 132^\circ \]

Now, divide by \(2\):

\[ m\angle B = 66^\circ \]

Thus, the measure of angle \(B\) in rhombus \(ABCD\) is \(66^\circ\).

The correct response is:

66°.