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# Two of a triangle's interior angles measure $45^{\circ}$ and $55^{\circ}$. If the triangle's side lengths are represented by a, b, and c and a<b<c, which of the following statements is true for this triangle? A. $a^{2}+b^{2}>c^{2}$, B. $a^{2}+b^{2}, C. $a^{2}+b^{2}=c^{2}$, D. Not enough information to determine.

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By Triangle Sum Theorem, the missing angle measures $180\text{\textdegree}-45\text{\textdegree}-55\text{\textdegree} =80\text{\textdegree}$. Since all angles are acute, then the triangle is an acute triangle.

By the Pythagorean acute inequality theorem, a triangle with side lengths $a$, $b$, and $c$ where $c$ is the longest side form an acute triangle if:

$a^2+b^2>c^2$

So, the correct answer is choice $\textbf{\color{#c34632}A.}$

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