Question
Shannon is asked to draw a quadrilateral with the following specifications:
two opposite angles measure 55°
adjacent angles are supplementary
a side length of seven inches
Which of the following statements about this quadrilateral is true?
A.
More than one quadrilateral exists with the given conditions, and all instances must be rhombuses.
B.
More than one quadrilateral exists with the given conditions, and all instances must be parallelograms.
C.
Exactly one quadrilateral exists with the given conditions, and it must be a rhombus.
D.
Exactly one quadrilateral exists with the given conditions, and it must be a parallelogram.
two opposite angles measure 55°
adjacent angles are supplementary
a side length of seven inches
Which of the following statements about this quadrilateral is true?
A.
More than one quadrilateral exists with the given conditions, and all instances must be rhombuses.
B.
More than one quadrilateral exists with the given conditions, and all instances must be parallelograms.
C.
Exactly one quadrilateral exists with the given conditions, and it must be a rhombus.
D.
Exactly one quadrilateral exists with the given conditions, and it must be a parallelogram.
Answers
GPT-4o mini
To analyze the specified quadrilateral, we have two opposite angles measuring 55° and all adjacent angles being supplementary. Here's how we can break down the conditions:
1. The quadrilateral has opposite angles of 55° each. Thus, the other two angles must sum to 180° (since adjacent angles are supplementary). Therefore, the other two angles will also be 125° each because:
- 180° - 55° = 125°.
2. Given the angles, we can conclude that the quadrilateral must be a parallelogram because in a parallelogram, opposite angles are equal and adjacent angles are supplementary.
3. Since only the angle measures are specified, and we have a side length of seven inches, this allows for multiple configurations of the parallelogram (different orientations and lengths of sides) that still adhere to the angle conditions. For example, we can have various pairs of sides whose lengths can vary, provided they conform to the internal angle checks.
Given these points, we can conclude:
- More than one quadrilateral satisfies these conditions given sides can vary while retaining the angle constraints.
- Since the conditions regarding the angles match that of a parallelogram but do not specify equal side lengths, the quadrilateral does not have to be a rhombus (which requires all sides to be equal).
Thus, the correct answer is:
**B. More than one quadrilateral exists with the given conditions, and all instances must be parallelograms.**
1. The quadrilateral has opposite angles of 55° each. Thus, the other two angles must sum to 180° (since adjacent angles are supplementary). Therefore, the other two angles will also be 125° each because:
- 180° - 55° = 125°.
2. Given the angles, we can conclude that the quadrilateral must be a parallelogram because in a parallelogram, opposite angles are equal and adjacent angles are supplementary.
3. Since only the angle measures are specified, and we have a side length of seven inches, this allows for multiple configurations of the parallelogram (different orientations and lengths of sides) that still adhere to the angle conditions. For example, we can have various pairs of sides whose lengths can vary, provided they conform to the internal angle checks.
Given these points, we can conclude:
- More than one quadrilateral satisfies these conditions given sides can vary while retaining the angle constraints.
- Since the conditions regarding the angles match that of a parallelogram but do not specify equal side lengths, the quadrilateral does not have to be a rhombus (which requires all sides to be equal).
Thus, the correct answer is:
**B. More than one quadrilateral exists with the given conditions, and all instances must be parallelograms.**