which polygon has an interior angle sum of 900°?
which polygon has an interior angle sum of 900°?
Answer
Explanation:
Step1: Recall the formula for interior - angle sum
The formula for the sum of interior angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides of the polygon.
Step2: Solve for $n$
Set $S = 900^{\circ}$, then $(n - 2)\times180^{\circ}=900^{\circ}$. Divide both sides by $180^{\circ}$: $n - 2=\frac{900^{\circ}}{180^{\circ}} = 5$. Add 2 to both sides: $n=5 + 2=7$. A polygon with 7 sides is a heptagon.
Answer:
The polygon with 7 sides (heptagon) has an interior - angle sum of $900^{\circ}$.