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