Final answer:
A triangle with a 60-degree angle is not necessarily equilateral; it could also be isosceles or scalene. An equilateral triangle has three equal angles, each measuring 60 degrees, but other triangles can have varied angles and side lengths.
Step-by-step explanation:
If a triangle has an angle of 60 degrees, it does not necessarily have to be equilateral. By definition, an equilateral triangle is one where all three angles are equal, and since the sum of the angles in any triangle is 180 degrees, each angle in an equilateral triangle measures 60 degrees. However, there are other types of triangles that may have one 60-degree angle but differ in the length of their sides and the measurement of their other angles.
An isosceles triangle could also have a 60-degree angle if the other two angles are of equal measure, meaning they could each be 60 degrees resulting in an equilateral triangle, or they could vary, resulting in an isosceles but not equilateral triangle. Moreover, a scalene triangle, which has all sides of different lengths, could have one angle measure 60 degrees, with the other two angles adding up to 120 degrees to complete the 180-degree sum.
In conclusion, merely having a single angle of 60 degrees in a triangle does not make it equilateral; it is the equality of all three interior angles that defines an equilateral triangle.