julia is studying the sum of interior angles in polygons. she creates polygons with 3,5,6,7 and 9 sides, and records the sum of the interior angles in each polygon in the table. Write an equation or inequality that represents the situation.
For a polygon of n sides, the sum of the interior angles
= 180(n-2)°
To represent the situation, we need to write an equation that relates the number of sides of a polygon with the sum of its interior angles.
Let's denote:
- n as the number of sides of the polygon,
- S as the sum of the interior angles.
From Julia's recordings, we have the following data:
Polygon with 3 sides (triangle): S = ___
Polygon with 5 sides: S = ___
Polygon with 6 sides: S = ___
Polygon with 7 sides: S = ___
Polygon with 9 sides: S = ___
To find the equation, we can look for a pattern in the data.
Let's start by observing that the sum of the interior angles of a polygon with n sides is given by the formula:
S = (n - 2) * 180 degrees.
Using this formula, we can calculate the sum of the interior angles for each polygon:
Polygon with 3 sides (triangle): S = (3 - 2) * 180 = 180 degrees
Polygon with 5 sides: S = (5 - 2) * 180 = 540 degrees
Polygon with 6 sides: S = (6 - 2) * 180 = 720 degrees
Polygon with 7 sides: S = (7 - 2) * 180 = 900 degrees
Polygon with 9 sides: S = (9 - 2) * 180 = 1260 degrees
As we can see, the sum of the interior angles follows the pattern:
S = (n - 2) * 180
Now, we can write the equation that represents the situation:
S = (n - 2) * 180
In this equation, n represents the number of sides and S represents the sum of the interior angles of the polygon.