Content

• To step
• Method 1 of 2: Using the formula
• Tips
• Necessities

A polygon is a closed figure with straight sides. At each vertex of a polygon, there is both an inside and outside angle, which corresponds to the inside and outside angles of the closed figure. Understanding the relationships between these angles is useful in a variety of geometric problems. In particular, it is useful to know how to calculate the sum of the interior angles in a polygon. This can be done with a simple formula or by dividing the polygon into triangles.

To step

Method 1 of 2: Using the formula

1. Draw up the formula for finding the sum of the interior angles. The formula is ${ displaystyle sum = (n-2) times 180}$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 find the sum of the inside angles of a hexagon, you count six sides.
2. Process the value for n{ displaystyle n}Solve for n{ displaystyle n}Draw the polygon whose angles you need to add. The polygon can have any number of sides and can be regular or irregular.
   • For example, if you need to find the sum of the inside angles of a hexagon, you can draw a hexagonal shape.
3. Pick one vertex. Call this vertex A.
   • A vertex is a point where two sides of a polygon meet.
4. Draw a straight line from point A to the vertex in the polygon. The lines must not intersect. You are going to make a number of triangles.
   • You don't have to draw lines to the adjacent vertices, because they are already connected by one side.
   • For example, for a hexagon you have to draw three lines, dividing the shape into four triangles.
5. Multiply the number of triangles you made by 180. Since there are 180 degrees in a triangle, multiplying the number of triangles in your polygon by 180 can find the sum of the inside angles of your polygon.
   • Since you divided the hexagon into four triangles, you calculate ${ displaystyle 4 times 180 = 720}$ and you get a total of 720 degrees inside the polygon.

Tips

• Check your work on paper using a protractor by adding the inside angles manually. Be careful when drawing the sides of the polygon, as they must be straight.

Necessities

• Pencil
• Paper
• Protractor (optional)
• Pen
• Eraser
• Ruler