Question

In ΔXYZ, m∠X = 43° and m∠Y = 44°. Which list has the sides of ΔXYZ in order from shortest to longest?
Answer
Multiple Choice Answers
YZ, comma, XY, comma, ZXYZ,XY,ZX
ZX, comma, XY, comma, YZZX,XY,YZ
ZX, comma, YZ, comma, XYZX,YZ,XY
XY, comma, ZX, comma, YZXY,ZX,YZ
YZ, comma, ZX, comma, XYYZ,ZX,XY
XY, comma, YZ, comma, ZXXY,YZ,ZX

Answer 1

In triangle ΔXYZ, the order of the sides corresponds to the order of the opposite angles. The larger angle opposite a side indicates that the side is longer.

Given:
- m∠X = 43°
- m∠Y = 44°

To find m∠Z:
\[
m\angle Z = 180° - m\angle X - m\angle Y = 180° - 43° - 44° = 93°
\]

Now we have:
- m∠X = 43° (opposite side YZ)
- m∠Y = 44° (opposite side ZX)
- m∠Z = 93° (opposite side XY)

The sides opposite the angles are:
- YZ (opposite angle X)
- ZX (opposite angle Y)
- XY (opposite angle Z)

Ordering by angle size:
- Angle X (43°) < Angle Y (44°) < Angle Z (93°)

Thus, the order of the sides from shortest to longest is:
- YZ (shortest, opposite 43°)
- ZX (medium, opposite 44°)
- XY (longest, opposite 93°)

Therefore, the correct order from shortest to longest is:
**YZ, ZX, XY**

None of the multiple-choice answers completely fit this order. Please check for a typographical error in the options provided. If the choices are intended to be correct, the closest option, based on the order of our analysis, is:
- **YZ, ZX, XY** would indeed be listed as YZ, ZX, XY.

Based on the provided format, if the correct answer listed directly resembles this or includes a typo variation, then select that answer.