which polygon has an interior angle sum of 1080°?
which polygon has an interior angle sum of 1080°?
Answer
Explanation:
Step1: Recall the formula
The sum of interior - angles of a polygon is given by $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides of the polygon.
Step2: Set up the equation
We are given that $S = 1080^{\circ}$, so we set up the equation $(n - 2)\times180^{\circ}=1080^{\circ}$.
Step3: Solve for $n$
Divide both sides of the equation by $180^{\circ}$: $n - 2=\frac{1080^{\circ}}{180^{\circ}}=6$. Then add 2 to both sides: $n=6 + 2=8$. A polygon with 8 sides is an octagon.
Answer:
The polygon with 8 sides (octagon) has an interior - angle sum of $1080^{\circ}$.