Angles in Polygons
B. Angles in Polygons
Recall that a polygon is an enclosed shape composed of connected straight line segments. Polygons with more than 4 sides are named by the number of sides they have using Greek or Latin prefixes.
| Name | Number of Sides |
|---|---|
| triangle |
3
|
| quadrilateral |
4
|
| pentagon |
5
|
| hexagon |
6
|
| heptagon |
7
|
| octagon |
8
|
| nonagon |
9
|
| decagon |
10
|
Polygons are also classified as either convex or concave polygons. All interior angles in a convex polygon will be less than 180°.
You will focus on convex polygons in this course.
You can use the triangle interior angles sum to determine the interior angles sum of a polygon.
Example 1
Use the triangle interior angles sum to determine the interior angles sum of a quadrilateral.
Any quadrilateral can be split into two triangles by drawing a diagonal.
Each triangle has an interior angle sum of 180°, and there are two triangles within a quadrilateral, so the interior angles sum of a quadrilateral is 2 × 180° = 360° .
Any quadrilateral has an interior angles sum of 360°.
A similar procedure can be used to determine the interior angles sums of other polygons.