Geometry

Question Analysis:
This question involves using syllogistic reasoning with the properties of parallelograms.
The main focus is on using the given facts about a parallelogram to draw a conclusion about the congruence of its opposite angles.

Key Concept Explanation:
The first statement gives a property of parallelograms (opposite sides are parallel).
The second statement shows the relationship between opposite - side parallelism and opposite - angle congruence in a quadrilateral.

Step - by - Step Solution:
Given:
Premise 1: If a quadrilateral is a parallelogram, then its opposite sides are parallel.
Premise 2: If a quadrilateral has opposite sides parallel, then its opposite angles are congruent.
Premise 3: Quadrilateral PQRS is a parallelogram.
Since PQRS is a parallelogram (Premise 3), by Premise 1, its opposite sides are parallel.
Then, because its opposite sides are parallel, by Premise 2, its opposite angles are congruent.
Angle P and angle R are opposite angles, so angle P is congruent to angle R.

Option Analysis:
Option A: As shown in the step - by...