SOLUTION: There's an octagon shape. The interior ratio is 1:2:2:3:3:4:4:5. Find the longest interior and the longest exterior

Algebra ->  Polygons -> SOLUTION: There's an octagon shape. The interior ratio is 1:2:2:3:3:4:4:5. Find the longest interior and the longest exterior       Log On


   

Question 1023335: There's an octagon shape. The interior ratio is 1:2:2:3:3:4:4:5. Find the longest interior and the longest exterior
Found 2 solutions by ikleyn, fractalier:
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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In such formulation it does not make sense.

I know what do you mean, and I know how to solve it.

But your formulation is INTENTLY INACCURATE, and I don't want work to make it accurate, because it is your responsibility.

So, if you want to get the problem solved, formulate it accurately and then resubmit.


Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
I'm thinking you mean
"There's an octagon shape. The interior ratio of angles is 1:2:2:3:3:4:4:5. Find the largest interior angle and the largest exterior angle."
If so...we continue...
If the ratio of angles is is 1:2:2:3:3:4:4:5, their sum can be expressed as
x + 2x + 2x + 3x + 3x + 4x + 4x + 5x = 24x
These angles sum to 1080 degrees, the total within every octagon.
Thus
24x = 1080
x = 45
That makes the largest interior angle 5x = 5(45) = 225 degrees.
The largest exterior angle is 180 - 45 = 135 degrees
The main problem with this analysis is that two of the angles aren't angles at all...4x = 4(45) = 180 degrees...not to mention angles greater than 180 are spurious...