The total interior angles of a pentagon = 540°

Each time we add a side (triangle to square, square to pentagon, pentagon to hexagon) we add another 180°.

Triangle to pentagon

Triangle		Square		Pentagon
$180°$	$+$	$180°$	$+$	$180°$	$=$	$540°$

The total internal angle of a pentagon = 540°

The total interior angles of a pentagon is 540 degrees

Now divide the total internal angle by the number of corners.

i.e. divide 540° by 5.

$540^circ/5=108^circ$

1		2		3		4		5
$108°$	$+$	$108°$	$+$	$108°$	$+$	$108°$	$+$	$108°$	$=$	$540°$