Question

In ΔUVW, m∠U = 85° and m∠V = 22°. Which list has the sides of ΔUVW in order from longest to shortest?
Answer
Multiple Choice Answers
UV, comma, VW, comma, WUUV,VW,WU
VW, comma, WU, comma, UVVW,WU,UV
WU, comma, VW, comma, UVWU,VW,UV
UV, comma, WU, comma, VWUV,WU,VW
WU, comma, UV, comma, VWWU,UV,VW
VW, comma, UV, comma, WUVW,UV,WU

Answer 1

To determine the order of the sides of ΔUVW from longest to shortest based on the given angles, we can use the property that in any triangle, the larger angle is opposite the longer side.

In ΔUVW, we have:
- m∠U = 85°
- m∠V = 22°

First, we can find m∠W by using the fact that the sum of angles in a triangle is 180°:

\[
m∠W = 180° - m∠U - m∠V
\]
\[
m∠W = 180° - 85° - 22°
\]
\[
m∠W = 73°
\]

Now we have:
- m∠U = 85° (opposite side UV)
- m∠V = 22° (opposite side VW)
- m∠W = 73° (opposite side WU)

Now we can order the sides based on the angles:
- The largest angle is m∠U (85°), so the opposite side UV is the longest.
- The next largest angle is m∠W (73°), so the opposite side WU is the second longest.
- The smallest angle is m∠V (22°), so the opposite side VW is the shortest.

Thus, the order of the sides from longest to shortest is:
**UV, WU, VW**

The correct answer is:
**UV, comma, WU, comma, VW**

Therefore, the corresponding option from your list is:
**UV, WU, VW**.