If N is the number of triangles of different shapes (i.e. not similar) whose angles are all integers (in degrees), what is N/100 ?

Step-by-step solution

aligned & x+y+z=180 & x^1+y^1+z^1=177 & Total = ¹⁷⁷⁺² C₂ Total = 179 178 2 =179 89 & Total =3!( )+3( )+ & =6( )+3( )+1 aligned For ( ), number of ways = 1 For ( ), 2 + =177 , number of ways = (88 cases) For , number of ways = 179 89-3 88-1 6 aligned & = 15931-265 6 & =2611 aligned So total way 2611+88+1=2700 Ans. 27