[br][br][b]Polygon[/b]: an enclosed plane figure comprising connected line segments.[br][b]Interior angle[/b]: the angle inside the polygon between two sides that meet at a vertex.[br][b][i]Convex [/i]polygon[/b]: a polygon whose interior angles are all less than 180 degrees.[br][b][i]Regular [/i]polygon[/b]: a polygon whose sides are all the same length. Its interior angles are also all congruent.[br][br]Polygons are named for the number of sides they have:[br][b]Triangle [/b]- 3 sides[br][b]Quadrilateral [/b]- 4 sides[br][b]Pentagon [/b]- 5 sides[br][b]Hexagon [/b]- 6 sides[br]etc.

Here is a triangle. Click and hold vertex B, drag it around, and watch what happens to the angles.

Let's try another polygon, this time a quadrilateral. Move vertex B and vertex C around. Watch what happens to the angles.

Here's one way to show the total of the interior angles of a quadrilateral. Draw a diagonal, which shows that a quadrilateral can be seen as if it were composed of two triangles. If each triangle's angles total 180 degrees, the quadrilateral (which is the two triangles put together) must have a total of 360 degrees.

Here's a diagram showing the pentagon visualized as three triangles, making the total of its interior angles [math]3\cdot180=540[/math]

There's a special kind of polygon called a regular polygon, where every side is the same length. In this case, not only can you calculate the total of the interior angles, you can calculate each individual angle, since you know the total, you know the number of angles, and you know the angles are all the same (are congruent). [br][br]Here's a regular hexagon. Its six angles total 720 degrees (four times 180). Since there are six of them, each must be 120 degrees. The general equation would be [math]a=180\cdot\frac{\left(n-2\right)}{n}[/math][br][br]Now have some fun - grab vertex A and move it around. What happens to the hexagon? What happens to its angles?