The ratio of the measure of the exterior angle and interior angle of a regular polygon is 2:9. Find the number of sides of the polygon.
2x + 9x = 180 Then 360/x = Answer. Just solve for x in the first one and plus it in.
But the problem is 11x= 180 gives you a mixed number. How do I solve that?
Hust leave x as an improper fraction and plug it into 360/x. It'll work.
let x is the exterior angle of the regular polygon x/180-x = 2/9 9x = 2(180-x) 9x = 360 - 2x x = 360/11 number of sides = 360/x = 360/(360/11) = 11
\[x = \frac{180}{11}\]\[\frac{360}{x} \implies 360 \times \frac{11}{180} \implies?\]
Using Calcmathlete's method I got 22 sides. Is that correct? P.S. I forgot how to do super fractions, that is why I could not do the mixed number thing at first.
Yes.
i think answer is wrong. you should get 11 using my method. i believe my method is correct
@rsadhvika You put in 360 by accident. \[\frac{360}{\frac{180}{11}}\]
i have put the whole solution. check it
|dw:1343067117396:dw|
Can you take a look at what I did above?
|dw:1343067152583:dw|
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