Question

Question

Use the image to answer the 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 which answer is correct and why

114°
114°

57°
57°

66°
66°

33°
33°
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Answer 1

In a rhombus, opposite angles are equal and consecutive angles are supplementary. Given that \( m\angle A = 114^\circ \), we can find \( m\angle B \).

Since the angles in a rhombus are supplementary, we have:

\[ m\angle A + m\angle B = 180^\circ \]

Substituting the known value:

\[ 114^\circ + m\angle B = 180^\circ \]

Now, solving for \( m\angle B \):

\[ m\angle B = 180^\circ - 114^\circ = 66^\circ \]

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

The correct answer is 66°.