For the following figure, name the longest and the shortest side of the triangle.

From the properties of the triangle, that side opposite to the greater angle is greater and the side opposite to the smaller angle is smaller.

The Sum of all sides of a triangle equals to 180 degrees.

Consider the figure $\Delta GHI$.

From the figure, the measure of angles are as follows:

$$\begin{gathered} \angle G={32}^{\circ } \\ \angle H={121}^{\circ } \end{gathered}$$

From angle sum property in a triangle, find the third angle as follows:

$$\begin{gathered} \angle G+\angle H+\angle I={180}^{\circ } \\ {32}^{\circ }+\angle I+{121}^{\circ }={180}^{\circ } \\ \angle B={180}^{\circ }-{153}^{\circ } \\ \angle B={27}^{\circ } \end{gathered}$$

From the properties of the triangle, that side opposite to the greater angle is greater and the side opposite to the smaller angle is smaller.

Then the greater angle is $\angle H$and the side opposite to $\angle H$is $GI$and the smaller angle is $\angle I$and the side opposite to $\angle I$is $GH$.

Therefore, the longest side is $GI$and the shortest side is $GH$.