question
in $ \triangle vwx, m\angle v = 102 ^ { \circ } $ and $ m\angle w = 51 ^ { \circ } $. which list has the sides of $ \triangle vwx $ in order from
shortest to longest?
answer
$ \bigcirc xv, vw, wx $
$ \bigcirc vw, wx, xv $
$ \bigcirc wx, vw, xv $
$ \bigcirc xv, wx, vw $
$ \bigcirc wx, xv, vw $
$ \bigcirc vw, xv, wx $

Question

Accepted Answer

# Explanation:
## Step1: Find the measure of angle $X$
The sum of angles in a triangle is $180^{\circ}$. So, $m\angle X=180^{\circ}-m\angle V - m\angle W$. Substituting $m\angle V = 102^{\circ}$ and $m\angle W=51^{\circ}$, we get $m\angle X=180^{\circ}-102^{\circ}-51^{\circ}=27^{\circ}$.
## Step2: Recall the side - angle relationship
In a triangle, the larger the angle, the longer the side opposite it.
Since $m\angle X = 27^{\circ}$, $m\angle W = 51^{\circ}$, and $m\angle V=102^{\circ}$, the sides opposite these angles are $VW$ (opposite $\angle X$), $XV$ (opposite $\angle W$), and $WX$ (opposite $\angle V$) respectively.
So, $VW<XV<WX$

# Answer:
VW, XV, WX

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QUESTION IMAGE

Question

Explanation:

Step1: Find the measure of angle \(X\)

Step2: Recall the side - angle relationship

Answer: