Geometry

Question Analysis:
This question focuses on applying syllogistic reasoning with the properties of equilateral triangles.
The main idea is to use the given conditional statements about equilateral triangles to draw a conclusion about triangle XYZ.

Key Concept Explanation:
The first statement defines an equilateral triangle in terms of side - equality.
The second statement shows the relationship between side - equality and angle - equality in a triangle.

Step - by - Step Solution:
Given:
Premise 1: If a triangle is equilateral, then all its sides are equal.
Premise 2: If all sides of a triangle are equal, then the triangle is equiangular.
Premise 3: Triangle XYZ is equilateral.
Since triangle XYZ is equilateral (Premise 3), by Premise 1, all its sides are equal.
Then, because all its sides are equal, by Premise 2, triangle XYZ is equiangular.

Option Analysis:
Option A: As shown in the step - by - step solution, triangle XYZ is equiangular, so this option is correct.