To find the order of the angle measures from smallest to largest, let's look at the given diagram and notice the marked lengths of the sides.
We can see that RT is the shortest side, followed by RS and then ST.
RT< RS< ST
⇕
4 < 5 < 7
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.
cc
Side & Opposite Angle [0.7em]
RT & ∠S [0.7em]
RS & ∠T [0.7em]
ST & ∠R
Therefore, we can list angles in order from smallest to largest.
m∠S < m∠T < m∠R
