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)ResponsesZY¯¯¯¯¯¯¯Modifying above upper Z upper Y with barXY¯¯¯¯¯¯¯¯Modifying above upper X upper Y with barZX¯¯¯¯¯¯¯¯Modifying above upper Z upper X with barYX¯¯¯¯¯¯¯¯Modifying above upper Y upper X with bar

Answer 1

To determine which side of triangle △XYZ would be listed last in increasing order, we first need to find the measure of the third angle, ∠Z.

The sum of the angles in a triangle is always 180°. Therefore, we can calculate ∠Z as follows:

\[ \angle Z = 180° - \angle X - \angle Y \] \[ \angle Z = 180° - 72° - 39° = 69° \]

Now we have the measures of all angles:

• ∠X = 72°
• ∠Y = 39°
• ∠Z = 69°

In a triangle, the length of the side opposite the largest angle is the longest side, and the length of the side opposite the smallest angle is the shortest side.

The angles in increasing order are:

• ∠Y = 39° (smallest)
• ∠Z = 69°
• ∠X = 72° (largest)

Now, we can identify the sides opposite these angles:

• The side opposite ∠Y (39°) is side XZ.
• The side opposite ∠Z (69°) is side XY.
• The side opposite ∠X (72°) is side YZ.

Since we are interested in the side that would be listed last when the sides are arranged in increasing order, we note that:

• Side XZ is the shortest (opposite the smallest angle).
• Side XY is of medium length.
• Side YZ is the longest (opposite the largest angle).

Thus, the side that would be listed last in increasing order is YZ.