To determine which quadrilaterals always have consecutive angles that are supplementary, we need to understand this property in the context of each given quadrilateral type:
- Parallelograms: In a parallelogram, consecutive angles are supplementary. This means the sum of any two consecutive angles is [tex]\(180^\circ\)[/tex].
- Rectangles: A rectangle is a type of parallelogram where all angles are [tex]\(90^\circ\)[/tex]. Since any pair of consecutive angles in a rectangle add up to [tex]\(180^\circ\)[/tex], they are supplementary.
- Rhombi: A rhombus is also a type of parallelogram. Hence, consecutive angles in a rhombus are supplementary as well.
- Squares: A square is a rectangle with all sides equal. Being a type of rectangle (and parallelogram), consecutive angles in a square are supplementary, each pair adding up to [tex]\(180^\circ\)[/tex].
- Kites: Kites have an adjacent pair of equal lengths, but they do not necessarily have supplementary consecutive angles. This means one diagonal bisects the other at right angles, and in general, kites do not always fulfill the supplementary consecutive angles property.
Given this analysis, we can answer the question:
A) II and IV only - refers to Rectangles and Squares only.
B) I and III only - refers to Parallelograms and Rhombi only.
C) I, II, III, and IV only - includes Parallelograms, Rectangles, Rhombi, and Squares.
D) I, II, III, IV, and V - includes all the options including Kites.
Since Kites do not necessarily have supplementary consecutive angles, options including Kites (like option D) are incorrect. Therefore, the correct answer is:
C. I, II, III, and IV only
This option correctly identifies the Parallelograms, Rectangles, Rhombi, and Squares as the quadrilaterals that always have supplementary consecutive angles.
