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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

114°
114°

57°
57°

66°
66°

33°
33°
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1 answer

In a rhombus, opposite angles are equal and adjacent angles are supplementary. Since angle A (m∠A) is given as 114°, we can determine angle B as follows:

  1. Since angles A and B are adjacent angles in the rhombus, their sum should be 180°: \[ m∠A + m∠B = 180° \]
  2. Plugging in the value of angle A: \[ 114° + m∠B = 180° \]
  3. To find angle B, we subtract 114° from 180°: \[ m∠B = 180° - 114° = 66° \]

Therefore, the measure of angle B (m∠B) of rhombus ABCD is 66°.