Final answer:
In a rectangle, square, and parallelogram, the diagonals bisect both sets of opposite angles. In a trapezoid and kite, the diagonals do not bisect both sets of opposite angles.
Step-by-step explanation:
In a quadrilateral, a diagonal is a line segment that connects two non-adjacent vertices.
To determine which quadrilateral diagonals do not bisect both sets of opposite angles, we need to consider the properties of each type of quadrilateral.
In a rectangle, both sets of opposite angles are congruent and bisected by the diagonals.
This is also true for a square and a parallelogram.
Therefore, the diagonals in these quadrilaterals bisect both sets of opposite angles.
In a trapezoid or a kite, the diagonals do not bisect both sets of opposite angles. In a trapezoid, one pair of opposite angles is congruent, but the other pair is not.
The diagonals bisect the congruent angles, but not the non-congruent ones.
In a kite, both pairs of opposite angles are congruent, but only one diagonal bisects both sets of opposite angles.
The other diagonal does not bisect both sets of opposite angles.