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°
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°` 