equiangular

Equiangular describes a figure whose angles are all equal. In polygons, an equiangular polygon has each interior angle equal to (n−2) × 180/n degrees, where n is the number of sides. For example, a rectangle is equiangular with interior angles of 90 degrees.

In triangles, equiangular implies equilateral, so the only equiangular triangle is the equilateral triangle. More generally, equiangular does not, by itself, guarantee equal side lengths: a polygon can be equiangular without being equilateral or regular.

A polygon that is equiangular and equilateral is called regular; thus regular polygons are a subset of equiangular polygons. However, most equiangular polygons (such as rectangles) are not regular because their side lengths vary.

The concept can also apply in other geometric contexts, where all angles formed by adjacent elements are equal. In higher dimensions or non-Euclidean settings, the precise meaning can differ and may require additional qualifications.

Summary: equiangular indicates uniformity of angles, most commonly in polygons. Its key consequence for an n-sided polygon is that each interior angle is (n−2) × 180/n degrees, with equality of angles not necessarily implying equality of side lengths.