Question

list the side lengths of $\triangle xyz$ in order from shortest to longest.

Explanation:

Step1: Sum angles to 180°

$$(a-33^\circ)+(2a-88^\circ)+(2a-99^\circ)=180^\circ$$

Step2: Simplify the equation

$$5a - 220^\circ = 180^\circ$$

Step3: Solve for $a$

$$5a=400^\circ \implies a=80^\circ$$

Step4: Calculate each angle

$\angle X = 80^\circ-33^\circ=47^\circ$
$\angle Y = 2(80^\circ)-88^\circ=72^\circ$
$\angle Z = 2(80^\circ)-99^\circ=61^\circ$

Step5: Match sides to opposite angles

Side opposite $\angle X$: $YZ$
Side opposite $\angle Y$: $XZ$
Side opposite $\angle Z$: $XY$
Order angles: $47^\circ<61^\circ<72^\circ$

Answer:

$YZ < XY < XZ$