Answer
$163.5^{\circ}$
Work Step by Step
Let $C$ be the angle opposite the longer diagonal.We need to use the law of cosines to find $C$.
$c^2 = a^2+b^2-2ab~cos~C \implies cos~C = \frac{a^2+b^2-c^2}{2ab} \\ C = arccos(\dfrac{a^2+b^2-c^2}{2ab})\\C = arccos(\dfrac{25.9^2+32.5^2-57.8^2}{(2)(25.9)(32.5)})\\ C = arccos(-0.9586)\\C = 163.5^{\circ}$
Thus, the angle opposite the longer diagonal is $163.5^{\circ}$.
