1. Lesson 3.3
Objective/Topic: Determine the sum of interior angles of a polygon. To determine the measures of exterior angles of a polygon.
Essential Question: What is the sum of the exterior angles of a polygon?
We know the sum of the interior angles of triangles and quadrilaterals.
Sum of the angles
180⁰
Sum of the angles is
360⁰

2. Draw a segment on the figure to create two triangles.
The sum of the angles in each triangle is 180⁰.
Therefore the sum of the angles of the rectangle is 360⁰.

3. Draw segments from a single vertex to divide polygon into triangles.
There are three triangles each with a sum of 180⁰
3 ∙ 180
Total sum of angles of pentagon is 540⁰

4. ≈128.57 Divide 900 by 7 to determine each angle.
Determine the sum of the interior angles of the regular figure.
7 Sides (n – 2) ∙ 180
(7 – 2) ∙ 180
5 ∙ 180
900⁰
Divide 900 by 7 to determine each angle.
≈128.57

5. Exterior Angles:

6. Find the measure of the exterior angle.

7. Z = 105 124 + z + 26 + z = 360 2z = 210 Determine the value of z

8. 1080 ÷ 8 Practice Each angle is 135⁰ (n – 2) ∙ 180 (8 – 2) ∙ 180
Determine the sum of interior angles in a regular Octagon.
(n – 2) ∙ 180
(8 – 2) ∙ 180
6 ∙ 180
1080
Then determine the measure of each of the angles.
1080 ÷ 8
Each angle is 135⁰