EQ: Tuesday, November 7, 2023

• How do I name polygons?

• What are the measures of the interior and exterior angles of polygons?

What are Polygons?

Any closed shape in a plane formed by 3 or more lines segments.

​Polygons

​Sides Name

​3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9+ 9-gon (etc)

Equilateral (or Regular) Polygons

Congruent Sides and Congruent Angles

Equilateral Triangle:

Equilateral Quadrilateral:

The sum of the interior angles in a triangle is 180°.

​6 Sides = 4 Triangles = 4 x 180 = 720

​6 Sides = 4 Triangles = 4 x 180 = 720








8 Sides = 6 Triangles = 6 x 180 = 1080

​The sum of the interior angles of a polygon is

6 Sides => Sum of angles = 180(6 - 2) = 720

720 – (40 + 160 + 120 + 100 + 150) = 150

What is the measure of the missing angle?

Find the measure of each angle in a regular heptagon (7 sides).

Sum of angles in a heptagon

S = 180(7 – 2) = 900

900 ÷ 7 ≈ 128.6o

128.6

​Exterior Angles of Polygons

​measured as the angle from the extended side of the interior angle

supplementary to the interior angle

128.6°

51.4°
Exterior

• ​Finding the sum of the interior angles of a polygon.

• Finding the measure of each interior angle in a regular polygon.

• Finding the measure of each exterior angle of a regular polygon.

• Finding the sum of the exterior angles in any polygon.

​Notes