regular nonagon 
  
    
      
        A
        B
        C
        D
        E
        F
        G
        H
        I
      
    
    {\displaystyle ABCDEFGHI}
  
 with 
  
    
      
        O
      
    
    {\displaystyle O}
  
 being the center of its circumcircle. Computing of the angles:

  
    
      
        
          
            
              
                
                  40
                  
                    ∘
                  
                
              
              
                
                =
                
                  
                    
                      360
                      
                        ∘
                      
                    
                    9
                  
                
              
            
            
              
                
                  70
                  
                    ∘
                  
                
              
              
                
                =
                
                  
                    
                      
                        180
                        
                          ∘
                        
                      
                      −
                      
                        40
                        
                          ∘
                        
                      
                    
                    2
                  
                
              
            
            
              
                α
              
              
                
                =
                
                  180
                  
                    ∘
                  
                
                −
                
                  90
                  
                    ∘
                  
                
                −
                
                  70
                  
                    ∘
                  
                
                =
                
                  20
                  
                    ∘
                  
                
              
            
            
              
                β
              
              
                
                =
                
                  180
                  
                    ∘
                  
                
                −
                
                  90
                  
                    ∘
                  
                
                −
                (
                
                  70
                  
                    ∘
                  
                
                −
                α
                )
                =
                
                  40
                  
                    ∘
                  
                
              
            
            
              
                γ
              
              
                
                =
                
                  140
                  
                    ∘
                  
                
                −
                β
                −
                α
                =
                
                  80
                  
                    ∘
                  
                
              
            
          
        
      
    
    {\displaystyle {\begin{aligned}40^{\circ }&={\frac {360^{\circ }}{9}}\\70^{\circ }&={\frac {180^{\circ }-40^{\circ }}{2}}\\\alpha &=180^{\circ }-90^{\circ }-70^{\circ }=20^{\circ }\\\beta &=180^{\circ }-90^{\circ }-(70^{\circ }-\alpha )=40^{\circ }\\\gamma &=140^{\circ }-\beta -\alpha =80^{\circ }\end{aligned}}}