Geometry

Question Analysis:
This problem requires using the adjacent angles property in parallelograms to solve for x and then find a specific angle measure.

Key Concept Explanation:
In parallelograms:
Adjacent angles are supplementary (sum to 180°)
Opposite angles are congruent (equal in measure)

Step-by-Step Solution:
Set up equation using adjacent angles: (5x - 20) + (3x + 40) = 180
Combine like terms: 8x + 20 = 180
Solve for x: 8x = 160 → x = 20
∠R is opposite ∠P:
First find ∠P = 5(20) - 20 = 80°
And opposite angles should be equal ...