Question

In ΔWXY, XY = 13, YW = 6, and WX = 17. Which statement about the angles of ΔWXY must be true?
Answer
Multiple Choice Answers
m, angle, W, is greater than, m, angle, X, is greater than, m, angle, Ym∠W>m∠X>m∠Y
m, angle, X, is greater than, m, angle, W, is greater than, m, angle, Ym∠X>m∠W>m∠Y
m, angle, Y, is greater than, m, angle, W, is greater than, m, angle, Xm∠Y>m∠W>m∠X
m, angle, Y, is greater than, m, angle, X, is greater than, m, angle, Wm∠Y>m∠X>m∠W
m, angle, X, is greater than, m, angle, Y, is greater than, m, angle, Wm∠X>m∠Y>m∠W
m, angle, W, is greater than, m, angle, Y, is greater than, m, angle, Xm∠W>m∠Y>m∠X

Answer 1

To determine the relationship between the angles in triangle ΔWXY based on the lengths of its sides, we can use the property that in any triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

In ΔWXY, we have the following side lengths:
- XY = 13
- YW = 6
- WX = 17

Now, we can compare the side lengths:
- The longest side is WX = 17.
- The middle side is XY = 13.
- The shortest side is YW = 6.

Now, using the property mentioned earlier:
- The angle opposite the longest side WX (which is 17) is angle Y (∠Y).
- The angle opposite the middle side XY (which is 13) is angle W (∠W).
- The angle opposite the shortest side YW (which is 6) is angle X (∠X).

Thus, we have the following relationships:
- Since WX (17) is the longest, ∠Y is the largest angle.
- Since XY (13) is the middle side, ∠W is the middle angle.
- Since YW (6) is the shortest, ∠X is the smallest angle.

From this, we can conclude:
\( m∠Y > m∠W > m∠X \)

So the correct answer is:
\( m∠Y > m∠W > m∠X \)