Alex thinks 131 degrees are neat

Alex thinks 131 degrees are neat. What is the maximum number of interior angles of a convex 190-gon that can have measure 131 degrees?

 

Angle sum of an  n  sided polygon is 180(n-2)

So the angle sum of 190gon (which i assume means 190 sides ) is

 

Sum of angles = 180*188 = 33840 degrees

All angles are less than 180 degrees

 

 

131x+180y<33480       x+y=190    x is the number of 131 degrees angles and y is the number of other angles.

solve simultaneously.

 

131x+180y=33480 (1)

    x   +  y   =  190    (2)

Solve simultaneously and round x and y down to the nearest integer

 

Then check your answer.    

 

I have not checked what i have said.  You need to do that.