Answer:
93.39
Step-by-step explanation:
So the sum of exterior angles of the convex octagon is: 360 degrees
This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x
[tex](x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)[/tex]
Group like terms
[tex](x+2x+3x+3x+2x+3x+3x+6x) + (14-3+8+16-17-4-12)[/tex]
Add like terms
[tex]23x+2[/tex]
Now let's set the sum of exterior angles to 360
[tex]23x+2 = 360[/tex]
Subtract 2 from both sides
[tex]23x=358[/tex]
Divide both sides by 23
[tex]x\approx 15.565[/tex]
So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one
Original equation
6x
Subsitute
6(15.565)
Simplify
[tex]93.39[/tex]
