To find the value of sin35 + cos40 + sin55 + cos20, we can use the trigonometric identities and the values of sine and cosine for specific angles.

sin35 = 0.5736
cos40 = 0.7660
sin55 = 0.8192
cos20 = 0.9397

Therefore, sin35 + cos40 + sin55 + cos20 = 0.5736 + 0.7660 + 0.8192 + 0.9397 = 3.0985.