Geometry

Question Analysis
This problem tests understanding of adjacent angle relationships in parallelograms and requires solving for an unknown angle using algebra.

Key Concept Explanation
In any parallelogram:
Adjacent angles are supplementary (sum to 180°)
Opposite angles are congruent
The sum of interior angles is always 360°

Step-by-Step Solution
Set up equation using adjacent angles property:
(2x + 15) + (3x - 25) = 180
Simplify and solve:
5x - 10 = 180 → 5x = 190 → x = 38
Find ∠A:
2(38) + 15 = 91°
Find ∠B:
3(38) - 25 = 89°
(Verification: 91° + 89° = 180°)
Determine ∠C (opposite ∠A):
∠C = ∠A = 91°

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