Geometry

Question Analysis:
This question involves identifying which angle-based conditions are enough to prove a quadrilateral is a parallelogram.
The main focus is on distinguishing sufficient vs. insufficient angle conditions.

Key Concept Explanation:
To prove a quadrilateral is a parallelogram, certain angle relationships can be used:
Sufficient conditions include:
Both pairs of opposite angles are congruent.
One angle is supplementary to both its adjacent angles.
Other facts (like all angles congruent or angle sum = 360°) are true for many quadrilaterals, not just parallelograms, so they are not sufficient.

Step-by-Step Solution:
A. Both pairs of opposite angles are congruent → ✅ Sufficient by definition.
B. All four angles are congruent → ✅ Same as option A.
C. One angle is supplementary to both adjacent angles → ✅ This guarantees the shape is a parallelogram.
D. One pair of opposite angles is congrue...