Question

In ΔXYZ, YZ = 12, ZX = 18, and XY = 7. Which list has the angles of ΔXYZ in order from largest to smallest?
Answer
Multiple Choice Answers
m, angle, Y, comma, m, angle, X, comma, m, angle, Zm∠Y,m∠X,m∠Z
m, angle, Z, comma, m, angle, Y, comma, m, angle, Xm∠Z,m∠Y,m∠X
m, angle, Z, comma, m, angle, X, comma, m, angle, Ym∠Z,m∠X,m∠Y
m, angle, Y, comma, m, angle, Z, comma, m, angle, Xm∠Y,m∠Z,m∠X
m, angle, X, comma, m, angle, Z, comma, m, angle, Ym∠X,m∠Z,m∠Y
m, angle, X, comma, m, angle, Y, comma, m, angle, Zm∠X,m∠Y,m∠Z

Answer 1

To determine the order of the angles in triangle ΔXYZ from largest to smallest, we can use the relationship between the lengths of the sides and the measures of the angles. Specifically, the longest side is opposite the largest angle, the second longest side is opposite the second largest angle, and the shortest side is opposite the smallest angle.

In triangle ΔXYZ:
- YZ = 12 (this side is opposite to angle X)
- ZX = 18 (this side is opposite to angle Y)
- XY = 7 (this side is opposite to angle Z)

Analyzing the side lengths, we have:
- ZX = 18 (longest side, opposite angle Y)
- YZ = 12 (second longest side, opposite angle X)
- XY = 7 (shortest side, opposite angle Z)

From this information, we can conclude:
- m∠Y (opposite ZX) is the largest angle.
- m∠X (opposite YZ) is the second largest angle.
- m∠Z (opposite XY) is the smallest angle.

Therefore, the order of the angles from largest to smallest is:
m∠Y, m∠X, m∠Z.

The correct choice is:
**m∠Y, m∠X, m∠Z**.