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
33°
33°
66°
66°
57°
57°
114°
114°
Skip to navigation
1 answer
In a rhombus, opposite angles are equal, and the adjacent angles are supplementary. Given that \( m∠A = 114° \), we can find \( m∠B \) as follows:
Since \( m∠A + m∠B = 180° \) (adjacent angles are supplementary), we can substitute the known angle into the equation:
\[ 114° + m∠B = 180° \]
Now, solve for \( m∠B \):
\[ m∠B = 180° - 114° \] \[ m∠B = 66° \]
Therefore, the measure of angle \( B \) is \( 66° \).
The correct response is:
66°
