Question

list the side lengths of $\triangle vwx$ in order from shortest to longest, given that $m\angle v = 38^\circ$, $m\angle x = 31^\circ$, and $m\angle w = 111^\circ$.
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Explanation:

Step1: Match angles to opposite sides

In $\triangle VWX$:

• $\angle V$ (38°) is opposite side $WX$
• $\angle X$ (31°) is opposite side $VW$
• $\angle W$ (111°) is opposite side $VX$

Step2: Order angles from smallest to largest

$31^\circ < 38^\circ < 111^\circ$, so $\angle X < \angle V < \angle W$

Step3: Relate to side lengths

In a triangle, shorter sides are opposite smaller angles. So the sides opposite the ordered angles follow the same order.

Answer:

$VW < WX < VX$