We know two angles of a triangle, ∠A = 65° and ∠B = 58°, and we have to identify the longest side.
The longest side will be the one that is opposite to the widest angle. In our case, we don't know the measure of C, but we know that the sum of the three measures has to be 180°, so we can calculate it as:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 65+58+m\angle C=180 \\ m\angle C=180-65-58 \\ m\angle C=57\degree \end{gathered}[/tex]
As the widest angle is at vertex A, the longest side will be its opposite, which correspond to the side formed by the other two vertices: B and C.
The longest side is BC.
