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?

Guest Oct 24, 2020

#3**+1 **

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.

Melody Oct 25, 2020