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

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.