What is the difference between an internal and an external angle?

A n internal angle of a polygon is the angle (the internal one) formed by two of its sides. The sum of all these angles can be easily calculated through the following formula: `S = (n - 2) xx 180` . It leads us to another conclusion: if the polygon is regular, all its internal angles have the same amplitude and so the measure of each one of those angles can be easily calculated by dividing the sum previously obtained by `n` (the number of the polygon sides). Let´s have a look at the following examples:

• The sum of all the internal angles: `S = (5 - 2) xx 180 = 3 xx 180 = 540º`
• Since the polygon is regular, each internal angle measures: `alpha = 540 : 5 = 108º`

• The sum of all internal angles: `S = (6 - 2) xx 180 = 4 xx 180 = 720º`
• Since the polygon is regular, each internal angle measures: `alpha = 720 : 6 = 120º`

Concerning the external angle, this one is formed by the extension of one of the sides of the polygon. The angle formed between the extended side and the opposite side corresponds to the external angle. If the polygon is regular, its external angles have all the same amplitudes. Thus, the measure of each one of those angles can be easily calculated by dividing 360º by `n` (the amount of the polygon sides).

• The sum of all the external angles: `360º`
• Since the polygon is regular, each external angle measures: `360 : 3 = 120º`

Is there any formula to calculate the sum of all the external angles?

While the internal angles have a formula to calculate the sum of all their angles, in this case it is not necessary, since the value of that sum is always 360º. Let’s have a look at the following animation in order to understand the reason why the sum of the external angles of every polygon is always the same.

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