This document discusses polygons, including defining their parts like vertices and diagonals. It explains how polygons are classified as either convex or concave based on angles. A key point is that the sum of the interior angles of any polygon can be calculated with the formula: (n - 2) x 180 degrees, where n is the number of sides. Some examples show how to use this formula to find the sum of interior angles or the measure of each interior angle for different polygons.

1. Angles
of a
Polygon

2. Objectives:
At the end of the lesson the learner will be
able to
Name the parts of a polygon and classify
them as either convex or concave
Classify polygons according to the
number of sides
Determine the sum of the measures of the
interior angles of a polygon

4. Parts of a Polygon
Four important terms related to a polygon:
Interior angle
Side
Vertex
Diagonal

7. Convex and Concave
Polygons
Polygons can be also be classified as either convex or
concave. Consider the following examples:

9. Sum of the Measures of
Interior Angles of Polygons

11. Example 2: Find the sum of the measures of interior
angles of an octagon.
Solution:
Sum of the measures of interior angles of a polygon
= (n – 2) ∙180°
Therefore, the sum of the measures of interior angles of
an octagon
= (8 – 2) ∙180°
= 6 ∙ 180°
= 1080°

12. Example 3: Find the measure of each interior
angle of a regular nonagon.

13. Example 4: The sum of the measures of
interior angles of a polygon is 1 440°. How
many sides does the polygon have?

14. Exterior Angles of a Polygon