Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 14: Quadrilaterals 193

Not right. If your vertices were A, B, C, D, and E, the diagonal from C to A is the same diagonal

you drew from A to C. In fact, there are only five diagonals in a pentagon because of that

duplication.

The hexagon has six starting places and three ending places, but again you have to divide by two

because of the duplicates. Six times three is 18, divided by two is nine diagonals in a hexagon.

If a polygon has n sides, it will have

nn 3

2

diagonals.

Sum of the Angles

The sum of the measures of the three angles of a triangle is 180r. A quadrilateral can be split into

two triangles by drawing one diagonal, and you can see that the total of the measurements of the

four angles in a quadrilateral is 360r. What about polygons with more sides?

If you draw all the diagonals from one vertex, you break the polygon up into triangles. In this

pentagon, drawing all the possible diagonals from one vertex divides the pentagon into three

triangles. The angles of the pentagon are split up, but adding up the angles of all the triangles

will make up the angles of the pentagon. The triangles each have a total of 180r so the total for

the three triangles is 540r. The total of the five interior angles of the pentagon is 540r.

The total number of degrees in the interior angles of a polygon with n sides is 180r times the

number of triangles you create by drawing the diagonals from one vertex. The number of

triangles is two less than the number of sides, so the total number of degrees is 180(n – 2).

A

DC

198

2 7

36

45

E B