To answer this question, we need to understand the properties of each quadrilateral.
Option A) Trapezium - In a trapezium, only one pair of opposite sides is parallel. Therefore, option A does not satisfy the condition that the opposite sides are parallel, so it is incorrect.
Option B) Rhombus - In a rhombus, all four sides are equal in length, so both pairs of opposite sides are the same length. However, a rhombus does not necessarily have opposite angles that are equal, so option B is incorrect.
Option C) Parallelogram - In a parallelogram, both pairs of opposite sides are parallel, so it satisfies condition b). Additionally, the opposite angles in a parallelogram are equal, so it satisfies condition c) as well. However, a parallelogram does not necessarily have all sides of equal length, so option C does not satisfy condition a).
Option D) Kite - In a kite, the opposite sides are not parallel, so option D does not satisfy condition b). Therefore, option D is incorrect.
Therefore, the correct answer is option C) Parallelogram. It is the only quadrilateral in which both pairs of opposite sides are parallel and the opposite angles are equal.