The total interior angles of an octagon = 1080°

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

Triangle to octagon

Triangle

Square

Pentagon

Hexagon

Heptagon

Octagon

$180°$

$+$

$180°$

$+$

$180°$

$+$

$180°$

$+$

$180°$

$+$

$180°$

$=$

$1080°$

The total internal angles of a heptagon = 1080°

The internal angles of an octagon equals 1080 degrees

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

i.e. divide 1080° by 8.

$1080^circ/8=135^circ$

1

2

3

4

5

6

7

8

$135°$

$+$

$135°$

$+$

$135°$

$+$

$135°$

$+$

$135°$

$+$

$135°$

$+$

$135°$

$+$

$135°$

$=$

$1080°$