Angles of a Polygon
Interior Angles
An interior angle or internal angle is determined by two consecutive sides.
Sum of Interior Angles of a Polygon
If n is the number of sides of a polygon:
S = (n − 2) · 180°.
Sum of interior angles of a triangle = (3 − 2) · 180° = 180º.
Sum of interior angles of a quadrilateral = (4 − 2) · 180° = 360º.
Sum of interior angles of a pentagon = (5 − 2) · 180° = 540º.
Sum of interior angles of a hexagon = (5 − 2) · 180° = 720º.
Angles of a Regular Polygon
Central Angle of a Regular Polygon
The central angle of a regular polygon is formed by two lines from consecutive vertices to the centre point or two radii of consecutive vertices of the circumsribed circle.
If n is the number of sides of a polygon:
Central angle = 360° : n
Central angle of the regular hexagon = 360° : 6 = 60º
Interior Angle of a Regular Polygon
The interior angle of a regular polygon is formed by two consecutive sides.
Interior angle = 180° − central angle
Interior angle of a regular hexagon = 180° − 60º = 120º
Exterior Angle of a Regular Polygon
The exterior angle of a regular polygon is formed by one side and the extension of the consecutive side.
The exterior and interior angles are supplementary, that is to say, that add up 180º.
Exterior angle = central angle
Exterior angle of the regular hexagon = 60º.
