Question

in δwxy, m∠w = 108° and m∠x = 39°. which list has the sides of δwxy in order from shortest to longest?
answer
○ yw, wx, xy ○ wx, yw, xy
○ wx, xy, yw ○ yw, xy, wx
○ xy, yw, wx ○ xy, wx, yw

Explanation:

Step1: Find the measure of angle Y

The sum of angles in a triangle is 180°. So, $m\angle Y=180^{\circ}-m\angle W - m\angle X$. Substituting the given values, $m\angle Y = 180^{\circ}-108^{\circ}-39^{\circ}=33^{\circ}$.

Step2: Recall the angle - side relationship in a triangle

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest.

Step3: Order the angles from smallest to largest

$m\angle Y = 33^{\circ}$, $m\angle X=39^{\circ}$, $m\angle W = 108^{\circ}$. So, $\angle Y<\angle X<\angle W$.

Step4: Order the sides from shortest to longest

The side opposite $\angle Y$ is $WX$, the side opposite $\angle X$ is $YW$, and the side opposite $\angle W$ is $XY$. So the order of the sides from shortest to longest is $WX, YW, XY$.

Answer:

WX, YW, XY