Final answer:
After calculating the measure of the third angle in triangle XYZ to be 24°, by applying Triangle Inequality Theorem, we can conclude that the length of the sides follow the order XY > YZ > ZX.
Step-by-step explanation:
The question asks us to determine the relationship between the sides of triangle XYZ given the measures of two of its angles. We know that the sum of angles in a triangle is always 180 degrees. Given m∠X = 104° and m∠Y = 52°, we can find the measure of angle Z using the equation:
104° + 52° + m∠Z = 180°
m∠Z = 180° - 156° = 24°
According to the Triangle Inequality Theorem, the larger the angle in a triangle, the longer the side opposite to it. Therefore, side XY, being opposite to the largest angle X, would be the longest side. Side YZ, opposite the next largest angle Y, would be the next in length, followed by side ZX, which is opposite the smallest angle Z. Thus, the correct statement about the sides of triangle XYZ is:
XY > YZ > ZX