Question

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.

Answer 1

2x + 9x = 180
Then
360/x = Answer.
Just solve for x in the first one and plus it in.

Answer 2

But the problem is 11x= 180 gives you a mixed number. How do I solve that?

Answer 3

Hust leave x as an improper fraction and plug it into 360/x. It'll work.

Answer 4

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

Answer 5

\[x = \frac{180}{11}\]\[\frac{360}{x} \implies 360 \times \frac{11}{180} \implies?\]

Answer 6

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.

Answer 7

Yes.

Answer 8

i think answer is wrong. you should get 11 using my method. i believe my method is correct

Answer 9

@rsadhvika You put in 360 by accident.
\[\frac{360}{\frac{180}{11}}\]

Answer 10

i have put the whole solution. check it

Answer 11

Can you take a look at what I did above?