Question

list the side lengths of $\triangle wxy$ in order from shortest to longest.\
the triangle $\triangle wxy$ has angles at $x$: $s + 27^\circ$, at $w$: $s + 46^\circ$, at $y$: $s + 56^\circ$.\
$\square < \square < \square$\
submit\
work it out\
not feeling ready yet? these can help:

Explanation:

Step1: Sum angles to find $s$

The sum of interior angles in a triangle is $180^\circ$.
$$(s+27)+(s+46)+(s+56)=180$$
$$3s + 129 = 180$$

Step2: Solve for $s$

Isolate $s$ by subtracting then dividing.
$$3s=180-129=51$$
$$s=\frac{51}{3}=17$$

Step3: Calculate each angle

Substitute $s=17$ into each angle expression.

• $\angle X = 17+27=44^\circ$
• $\angle W = 17+46=63^\circ$
• $\angle Y = 17+56=73^\circ$

Step4: Match angles to opposite sides

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

• Shortest side: Opposite $\angle X$ ($44^\circ$) is $WY$
• Middle side: Opposite $\angle W$ ($63^\circ$) is $XY$
• Longest side: Opposite $\angle Y$ ($73^\circ$) is $WX$

Answer:

$WY < XY < WX$