How to Calculate the Sum of Interior Angles

Step-by-Step Guide

1. 1

   Step 1: Set up the formula for finding the sum of the interior angles.

   The formula is sum=(n−2)×180{\displaystyle sum=(n-2)\times 180}, where sum{\displaystyle sum} is the sum of the interior angles of the polygon, and n{\displaystyle n} equals the number of sides in the polygon.The value 180 comes from how many degrees are in a triangle.
   
   The other part of the formula, n−2{\displaystyle n-2} is a way to determine how many triangles the polygon can be divided into.
   
   So, essentially the formula is calculating the degrees inside the triangles that make up the polygon.This method will work whether you are working with a regular or irregular polygon.
   
   Regular and irregular polygons with the same number of sides will always have the same sum of interior angles, the difference only being that in a regular polygon, all interior angles have the same measurement.In an irregular polygon, some of the angles will be smaller, some of the angles will be larger, but they will still add up to the same number of degrees that are in the regular shape.
2. 2

   Step 2: Count the number of sides in your polygon.

   Remember that a polygon must have at least three straight sides.
   
   For example, if you want to know the sum of the interior angles of a hexagon, you would count 6 sides. , Remember, n{\displaystyle n} is the number of sides in your polygon.
   
   For example, if you are working with a hexagon, n=6{\displaystyle n=6}, since a hexagon has 6 sides.
   
   So, your formula should look like this:sum=(6−2)×180{\displaystyle sum=(6-2)\times 180} , To do this, subtract 2 from the number of sides, and multiply the difference by
   180.
   
   This will give you, in degrees, the sum of the interior angles in your polygon.
   
   For example, to find out the sum of the interior angles of a hexagon, you would calculate:sum=(6−2)×180{\displaystyle sum=(6-2)\times 180}sum=(4)×180{\displaystyle sum=(4)\times 180}sum=(4)×180=720{\displaystyle sum=(4)\times 180=720}So, the sum of the interior angles of a hexagon is 720 degrees.
3. 3

   Step 3: Plug the the value of n{\displaystyle n} into the formula.

4. 4

   Step 4: Solve for n{\displaystyle n}.

Detailed Guide

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