The sum of the interior angles of the 5-sided polygon is 31/9 sides.
Let's find the number of sides of a polygon if the sum of its angles is 260°.
We can use the formula for the sum of angles in a polygon:
S=180 (n−2)
where:
S is the sum of the angles in the polygon
n is the number of sides in the polygon
We are given that the sum of the angles in the polygon is 260 degrees. We need to find the number of sides n.
Steps to solve:
1. Substitute the given value of S into the formula:
260 =180 (n−2)
2. Distribute the 180 degrees on the right side:
260 =180 n−360
3. Add 360 degrees to both sides to isolate n:
260 +360 =180 n
620 =180 n
4. Divide both sides by 180 degrees to solve for n:
620 /180 = 180n /180
n= 31/ 9
The polygon has 31/9 sides.
Question
The sum S of the angles of a polygon with n nmber of sides is given by the formula S=180°(n-2). How many sides has a polygon if the sum of its angles is 260°? Construct an inverse function to determine the result.