We want to use the given angle measurements of △ XYZ to compare the side lengths of the same triangle.
m∠ X= 51^(∘), m∠ Y= 59^(∘), m∠ Z=70^(∘)
Before we attempt to order the sides of the triangle, let's draw it so that we can visualize the relationship between the sides and the angles.
We know that, if two angles of a triangle are notcongruent, then the longer side lies opposite the larger angle. Applying this rule to our triangle, we can order the sides from shortest to longest.
ccccc
51^(∘) & < & 59^(∘) & < & 70^(∘)
m∠ X & < & m∠ Y & < & m∠ Z
YZ & < & XZ & < & YX
