Answer:
Equivalent equation of [tex]s =180(n-2)[/tex] is [tex]n =\frac{s}{180}+2[/tex]
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: [tex]s =180(n-2)[/tex] .....[1]
where n is the number of sides.
We can write the equivalent equation of [1]
[tex]s = 180(n-2)[/tex]
Divide both sides by 180;
[tex]\frac{s}{180} =\frac{180(n-2)}{180}[/tex]
Simplify:
[tex]\frac{s}{180}=n-2[/tex]
Add 2 to both sides of an equation:
[tex]\frac{s}{180}+2=n-2+2[/tex]
Simplify, we get;
[tex]n =\frac{s}{180}+2[/tex] ......[2]
Now, to find the value of n ;
Given: s =1260°
Substitute this value in [2] we get;
[tex]n =\frac{1260}{180}+2[/tex]
or
n = 7+2 =9
Therefore, the number of sides in a polygon is, n=9
