Convex polygons
Polygons in which the inside angle of every vertex is less than or equal to 180°.
A convex polygon is a closed geometric figure with straight sides and angles that do not bend inward. It means that all of its interior angles are less than 180 degrees, and all of its vertices point outward. The shape of the polygon does not matter, but it must not have any concavity.
Convex polygons have several properties:
1. All internal angles are less than 180 degrees: In a convex polygon, all interior angles must be less than 180 degrees. If any angle is greater than 180 degrees, then the polygon is not convex.
2. All sides are contained within the polygon: A convex polygon’s sides shall be contained entirely within the polygon itself.
3. All vertices point outward: In convex polygons, all vertices must point outward or lie on the boundary of the polygon.
4. Diagonals do not leave the polygon: One of the distinctive features of convex polygons is that none of its diagonals lay outside of the polygon.
5. The sum of exterior angles adds to 360 degrees: The exterior angles of the convex polygon can be defined as the angle between a side of the polygon and a straight line extended from the previous side. The sum of all these exterior angles of a convex polygon is always equal to 360 degrees.
Examples of convex polygons include squares, triangles, regular pentagons, and hexagons. Convex polygons have a wide range of uses. They are commonly used in graphic design, architecture, and engineering. For example; in architectural planning, regular convex polygons can be used to design buildings with symmetrical shapes.
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