A polygon is a shape with three or more straight sides.
Types of Polygons
A convex polygon has no interior angles greater than 180°
A concave polygon has one or more interior angles greater than 180°.
A regular polygon has all sides and all angles equal.
e.g. a regular hexagon.
Angles of Polygons
The exterior angles of any polygons add up to 360°.
e.g. a + b + c + d = 360o
The interior angles of a polygon have different sums depending on the number of sides in the polygon.
For a polygon with n sides: the sum of the interior angles = (n − 2) x 180°
e.g. For a 5-sided polygon (called a pentagon)
the interior angles add up to ( 5 − 2) x 180 = 540°
- Each polygon can be split into triangles:
Three triangles can be drawn.
Total interior angles of three triangles = 3 x 180° = 540o
Regular Polygons
The table summarises the names and angles of the more common regular polygons.
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180 − 120 = 60° |
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180 − 90 = 90° |
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180 − 72 = 108° |
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180 − 60 = 120° |
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180 − 45 = 135° |
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180 − 36 = 144° |
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n − gon |
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180 − |
