A convex vertex has an interior angle of less than 180 degrees. Whenever all the vertices of the polygon are convex, a line drawn across the polygon will never cross more than two sides. A polygon in which all the vertices are convex is called a convex polygon. In simple language, a convex vertex points outward from the center of the polygon. All polygons must have at least some convex vertices. In a triangle, all of the vertices will be convex.
A concave vertex of a polygon has an interior angle of more than 180 degrees. The vertex points toward the interior of the polygon rather than away from it. A line drawn across the two sides of a concave vertex will always cross more than two sides of the polygon. Many polygons do not have concave vertices. A triangle will never have a concave vertex.
Acute vertices, a subset of convex vertices, have an interior angle of less than 90 degrees. At least two, and sometimes three, acute vertices are found in all triangles and non-rectangular quadrilaterals. Acute vertices are much less common in polygons with more than four sides, unless there are also concave vertices in the polygon. The reason for this is each additional side and vertex of a polygon adds another 180 degrees to the total of interior angular degrees of the polygon.
Right vertices, a subset of convex vertices, have an interior angle of exactly 90 degrees. A triangle may have one right vertex, while polygons with more sides and vertices may have more than one side with a right angle. The rectangle (including the square) is the only polygon that contains only right vertices.
Obtuse vertices, a subset of convex vertices, have an interior of more than 90 degrees. A triangle may have only one obtuse vertex. Parallelograms, but not rectangles, may have two obtuse vertices. Obtuse angles occur more frequently in polygons with more than four sides. In fact, if the shape is a regular polygon, meaning all sides and vertices are equal, then all the vertices are obtuse if the polygon has five or more sides.