Exploring polygons and their angles reveals a world of geometric principles. Regular polygons have congruent sides and angles, with the sum of interior angles determined by the formula (n-2)×180°. This text delves into calculating individual angles in regular polygons, understanding exterior angles, and their constant sum of 360 degrees. These insights are essential for geometry and practical applications in various fields.
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Polygons are flat, two-dimensional figures with straight sides and angles
Definition of regular polygons
Regular polygons have congruent sides and angles
Examples of regular polygons
Examples of regular polygons include equilateral triangle, square, and regular hexagon
The sum of interior angles of a polygon can be calculated using the formula (n-2)×180°, where 'n' is the number of sides
The sum of interior angles increases with the number of sides, following the formula (n-2)×180°
Individual interior angles of a regular polygon can be found by dividing the sum of all interior angles by the number of sides
Calculating interior angles is useful in geometric design and pattern creation
Exterior angles are formed when one side of a polygon is extended and the angle between this extended line and the adjacent side is measured
The sum of an interior angle and its adjacent exterior angle is always 180 degrees
Understanding exterior angles is useful for calculating unknown angles in a polygon
The sum of exterior angles in a polygon is always 360 degrees
Knowing the sum of exterior angles can help solve geometric problems, such as determining the number of sides in a regular polygon
00
Regular ______ have all sides and ______ of equal measure, and the term originates from Greek words meaning 'many' and '______'.
polygons
angles
angle
01
Sum of interior angles for a triangle
Always 180 degrees
02
Sum of interior angles for a quadrilateral
Always 360 degrees
