Question

Lakeesha draws a triangle and labels it △XYZ. She knows ∠X=72° and ∠Y=39°. If the sides of the given triangle were listed in increasing order, which side would be listed last?(1 point) Responses YX¯¯¯¯¯¯¯¯ Modifying above upper Y upper X with bar ZY¯¯¯¯¯¯¯ Modifying above upper Z upper Y with bar ZX¯¯¯¯¯¯¯¯ Modifying above upper Z upper X with bar XY¯¯¯¯¯¯¯¯

Answer 1

To determine which side of triangle \( \triangle XYZ \) would be listed last when the sides are arranged in increasing order, we need to consider the relationship between the angles and the sides of the triangle.

In any triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

1. Calculate the remaining angle \( \angle Z \):
\[
\angle Z = 180° - \angle X - \angle Y = 180° - 72° - 39° = 69°
\]

2. Now we have the angles:
- \( \angle X = 72° \)
- \( \angle Y = 39° \)
- \( \angle Z = 69° \)

3. Compare the angles:
- \( \angle Y = 39° \) (smallest)
- \( \angle Z = 69° \)
- \( \angle X = 72° \) (largest)

4. According to the relationship between the sides and angles:
- The side opposite the smallest angle ( \( \angle Y \) ) is the shortest side, which is \( \overline{XZ} \).
- The side opposite the largest angle ( \( \angle X \) ) is the longest side, which is \( \overline{YZ} \).

Since \( \overline{YZ} \) is opposite the largest angle \( \angle X \), it will be the longest side.

Thus, if the sides were listed in increasing order, \( \overline{YX} \), \( \overline{ZX} \), \( \overline{ZY} \), and \( \overline{XY} \), the last side in the order will be:

**ZY (or \(\overline{YZ}\))**