Internal Angles of Regular Polygon
Jump to navigation
Jump to search
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:
- $A = 180 \degrees - \dfrac {360 \degrees} n$