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 a b c or d which one is it and why

114°
114°

57°
57°

66°
66°

33°
33°
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Answer 1

In a rhombus, opposite angles are equal, and the diagonals bisect the angles. Since \( \angle A = 114° \), then \( \angle C \) (the angle opposite to \( \angle A \)) is also \( 114° \).

The angles \( \angle B \) and \( \angle D \) are the remaining angles in the rhombus, and they are also equal to each other (since they are opposite angles).

To find \( \angle B \), we can use the property that the sum of all angles in any quadrilateral is \( 360° \). Thus, we find:

\[ \angle A + \angle B + \angle C + \angle D = 360° \]

Substituting the known angles:

\[ 114° + \angle B + 114° + \angle B = 360° \] \[ 228° + 2\angle B = 360° \] \[ 2\angle B = 360° - 228° \] \[ 2\angle B = 132° \] \[ \angle B = \frac{132°}{2} = 66° \]

Thus, the measure of angle \( \angle B \) is \( 66° \).

The correct response is: 66°