Exercise 5 Page 348

To find the order of the angle measures and sides from smallest to largest, let's look at the given diagram and notice the marked lengths of the sides.

We can see that $\overline{BC}$ is the shortest side, followed by $\overline{AB}$ and then $\overline{AC}.$ Next, let's consider Theorem $5.9$ about Angle-Side Relationships in Triangles.

Angle-Side Relationships in Triangles

If one side of a triangle is longer than another side, then the angle opposite the longer side has greater measure than the angle opposite the shorter side.

Now we need to think about the sides, and the corresponding opposite angles. Therefore, we can list the angles in order from smallest to largest.