Understanding Complex Shapes

There are many steps to understanding and identifying complex shapes. The first step is differentiating between the different types of shapes there can be in one family. For example, the polygon has three different classes. The first is the equilateral polygon in which all sides are congruent. The second class, the equiangular polygon, has angles which are all congruent. And the third is the regular polygon which is characterized by being a convex polygon that is both equiangular and equilateral.

Another step is understanding the different angles and measures in shapes. For example, in polygons there are three types of angles. The first is the interior angle (A) which is the inner part of the angle, the second is the exterior angle (B) which lies on the outside of the shape. The last type of angle is the central angle (C) which is measured by a vertex at the circles center creating adjacent line segments.

Angles in a Polygon

The third step to understanding complex shapes is being able to calculate their angles. There is a formula that allows you to do this with the different types of angles in polygons. In the formulas n=number of angles:

-Interior angle (A)

•     (n-2)x180/n

-Exterior angle (B)

•    360/n

-Central angle (C)

•    360/n

Hexagon Example:

(A)  (6-2)x180/6 = 120 degrees

(B)  (360/6) = 60 degrees

(C)  (360/6) = 60 degrees