Definition: The word "acute" and its definition are related to a special type of shape called an acute angle. A regular polygon (like a triangle) has six sides, which means it can be divided into 180° segments of equal length. A regular polygon is also called an equilateral or equiangular polygon because all the angles in any given regular polygon measure exactly 60°. However, in many cultures, a regular polygon with 360° (like a circle) has more than one side and angles. In such polygons, the sum of all interior angles is equal to 540°, which gives us an example of a regular pentagon (with five sides and five angles). This type of polygon also has 360° because it can be divided into 180° segments of equal length. So in summary: - "Acute" refers to an angle that measures less than 90°. - An acute angle is a regular polygon with more than one side and angles, meaning all its interior angles add up to 540° or 360°, but the sum of all exterior angles does not. As such: - Acute (angle less than 90°) - Acute Angle: All angles in a regular polygon are less than 90° and can be any angle - Hexagon: 5 sides, each equal to 60°; 12 total interior angles = 720° - Pentagon: 5 sides, each equal to 360° (also 360° of one regular polygon); 540° total interior angles = 720° - Circle: 360°, all angles are congruent; not a regular polygon because it has 360° but does have exactly 360° of sides (the number of sides is odd) - Regular Hexagon: All interior angles are equal (54° each) and all exterior angles are also 54°; 720° total interior angles = 180° (each side equals 90°) + 360° = 540° - Regular Pentagon: Interior angles are the same as hexagon, but not congruent (all sides equal and all exterior angles equal); 540° total interior angles = 720° These definitions are very general and can be applied to various polygons of different shapes.

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