Internal Angles of Regular Polygon

Theorem

The size $A$ of each internal angle of a regular $n$-gon is given by:

$A = \dfrac {\paren {n - 2} 180 \degrees} n$

Corollary

The internal angles of a square are right angles.

Proof

From Sum of Internal Angles of Polygon, we have that the sum $S$ of all internal angles of a $n$-gon is:

$S = \paren {n - 2} 180 \degrees$

From the definition of a regular polygon, all the internal angles of a regular polygon are equal.

Therefore, the size $A$ of each internal angle of a regular polygon with $n$ sides is:

$A = \dfrac {\paren {n - 2} 180 \degrees} n$

$\blacksquare$

Also presented as

This formula can also be seen presented as:

$A = 180 \degrees - \dfrac {360 \degrees} n$