To determine the number of sides of a regular polygon given that the sum of its interior angles is 1080°, let's go through the problem step-by-step.
1. Understanding the Sum of Interior Angles:
The formula to calculate the sum of the interior angles of a polygon with `n` sides is:
[tex]\[
\text{Sum of interior angles} = (n - 2) \times 180°
\][/tex]
2. Substituting the Given Sum:
According to the problem, the sum of the interior angles is 1080°. Thus we can set up the equation:
[tex]\[
(n - 2) \times 180° = 1080°
\][/tex]
3. Solving for [tex]\( n \)[/tex]:
Let's isolate [tex]\( n \)[/tex] by following these algebraic steps:
[tex]\[
(n - 2) \times 180° = 1080°
\][/tex]
Divide both sides by 180°:
[tex]\[
n - 2 = \frac{1080°}{180°}
\][/tex]
Simplifying the right-hand side:
[tex]\[
n - 2 = 6
\][/tex]
Finally, add 2 to both sides to solve for [tex]\( n \)[/tex]:
[tex]\[
n = 6 + 2
\][/tex]
[tex]\[
n = 8
\][/tex]
4. Conclusion:
The number of sides of the polygon is 8. Therefore, the correct answer is:
(d) 8
