Answer:
The polygon has 9 sides
Step-by-step explanation:
We need to equate the given expression to the given value and solve for n.
The sum of the interior angles, s, in an n-sided polygon is given by the expression:
[tex]s = 180(n - 2)[/tex]
We want to use this formula, to calculate how many sides has a polygon if the sum of the interior angles is 1,260°.
We solve the following equation for n.
[tex]180(n - 2) = 1260[/tex]
Divide through by 180 to get:
[tex] \frac{180(n - 2)}{180} = \frac{1260}{180} [/tex]
[tex]n - 2 = 7[/tex]
Add 2 to both sides to get:
[tex]n = 7 + 2[/tex]
[tex] \therefore \: n = 9[/tex]
Hence the polygon has 9 sides
