In which type of triangle are all angles equal?

An equilateral triangle is defined as a triangle in which all three sides are of equal length. This inherent property leads to all angles also being equal. Specifically, since the sum of the interior angles in any triangle is 180 degrees, each angle in an equilateral triangle measures 60 degrees. This uniformity in side lengths and angles is what distinguishes an equilateral triangle from other types of triangles.

In contrast, an isosceles triangle has at least two sides of equal length, which means it has at least two angles that are also equal, but it does not guarantee that all angles are equal. A scalene triangle, by definition, has all sides of different lengths, so all angles are also different. A right triangle has one angle that is exactly 90 degrees, while the other two angles must be acute and complementary, making them unequal.

Overall, the defining characteristic of an equilateral triangle is that all angles are not only equal but also result from the equal lengths of its sides, making it the correct choice for this question.