Answer:
Equivalent equation of
is
And the number of sides does a polygon have is, n =9.
Step-by-step explanation:
Given:
The sum of the interior angles, 's' in a n-sided polygon can be determined
using the formula is:
.....[1]
where n is the number of sides.
We can write the equivalent equation of [1]
![s = 180(n-2)](https://tex.z-dn.net/?f=s%20%3D%20180%28n-2%29)
Divide both sides by 180;
![\frac{s}{180} =\frac{180(n-2)}{180}](https://tex.z-dn.net/?f=%5Cfrac%7Bs%7D%7B180%7D%20%3D%5Cfrac%7B180%28n-2%29%7D%7B180%7D)
Simplify:
![\frac{s}{180}=n-2](https://tex.z-dn.net/?f=%5Cfrac%7Bs%7D%7B180%7D%3Dn-2)
Add 2 to both sides of an equation:
![\frac{s}{180}+2=n-2+2](https://tex.z-dn.net/?f=%5Cfrac%7Bs%7D%7B180%7D%2B2%3Dn-2%2B2)
Simplify, we get;
......[2]
Now, to find the value of n ;
Given: s =1260°
Substitute this value in [2] we get;
or
n = 7+2 =9
Therefore, the number of sides in a polygon is, n=9