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°
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°` 
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°
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°` 