Question

in $delta uvw$, $mangle u = 85^{circ}$ and $mangle v = 22^{circ}$. which list has the sides of $delta uvw$ in order from longest to shortest? answer
○ uv, vw, wu
○ wu, vw, uv
○ wu, uv, vw
○ vw, wu, uv
○ uv, wu, vw
○ vw, uv, wu

Explanation:

Step1: Find angle W

The sum of angles in a triangle is 180°. So, $m\angle W=180^{\circ}-m\angle U - m\angle V=180^{\circ}-85^{\circ}-22^{\circ}=73^{\circ}$.

Step2: Recall angle - side relationship

In a triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle.
Since $m\angle U = 85^{\circ}$, $m\angle W=73^{\circ}$, $m\angle V = 22^{\circ}$, the side opposite $\angle U$ is $VW$, the side opposite $\angle W$ is $UV$, and the side opposite $\angle V$ is $WU$.
So the sides from longest to shortest are $VW$, $WU$, $UV$.

Answer:

VW, WU, UV