Answer
$128^{\circ}$
Work Step by Step
The largest angle in the triangle is opposite to the longest side
From figure, largest angle is A.
using law of cosines
$a^2= b^2+c^2-2bc \cos A$
$\cos A =\frac{b^2+c^2-a^2}{2bc}$
$\cos A=\frac{10^2+31^2-38^2}{2\times 10\times 31}$
$\cos A =-0.618$
$A=\cos^{-1}(-0.618)$
$A=128^{\circ}$
