Sure! Let's carefully analyze the given properties of the quadrilateral and determine which option correctly describes it.
### Step-by-Step Solution:
1. Identifying the Properties:
- Two pairs of adjacent sides equal: This means that in the quadrilateral, two consecutive sides are equal to each other, and another two consecutive sides are equal to each other (but not necessarily equal to the first pair).
- Opposite angles between the unequal sides are equal: This means that the angles between the pairs of unequal sides are equal. In other words, if you look at the angles formed at the vertices where the unequal sides meet, those angles are equal.
2. Analyzing Each Option:
- Option A: Parallelogram
- A parallelogram has opposite sides equal and parallel. Although the opposite angles are equal, the condition of adjacent sides being equal does not apply here. Moreover, the angles between unequal sides being equal is not a characteristic specific to parallelograms in general.
- Option B: Rhombus
- A rhombus has all four sides equal. While it meets the condition that opposite angles are equal, it does not fit the property of having two pairs of adjacent sides that are equal and two pairs that are unequal.
- Option C: Kite
- A kite has two pairs of adjacent sides that are equal. It also has one pair of opposite angles that are equal (the angles between the unequal sides). Therefore, it perfectly matches the given properties.
- Option D: Trapezium (or Trapezoid)
- A trapezium has only one pair of opposite sides parallel and no specific requirement about side lengths or angles that match the given properties.
3. Conclusion:
- Based on the given properties (two pairs of adjacent sides being equal and opposite angles between the unequal sides being equal), the correct quadrilateral is a Kite.
Thus, the correct answer is:
Option C: Kite
