1. Lesson 8-1
Angles of Polygons
Lesson 3-4: Polygons

2. Convex Polygon Diagonals
Diagonals of a Polygon:
A segment connecting nonconsecutive vertices of a polygon
Determine the least number of triangles that can be formed from each polygon by drawing diagonals. What correlation can be made between the number of triangles and the number of sides of the polygon?
Lesson 3-4: Polygons

3. 3 sides 4 sides 5 sides 6 sides 8 sides
Determine the least number of triangles that can be formed from each polygon by drawing diagonals. What correlation can be made between the number of triangles and the number of sides of the polygon?
3 sides sides sides sides sides
__triangle __ triangles __ triangles __ triangles __triangles
____° ____° ____° ____ ° ____ °
The number of triangles is:
If the sum of the interior angles of a triangle is 180°, what can we assume to be the sum of the interior angles of the polygons shown?
What is the formula to find the sum of the interior angles of a convex polygon?
Lesson 3-4: Polygons

4. Find the sum of the interior angles of each convex polygon.
S = n = # of sides
A) Quadrilateral
B) 11-gon
Lesson 3-4: Polygons

5. Find the measure of each interior angle using the given information.
(6x – 4)°
(2x + 8)°
(2x + 8)°
(6x – 4)°
Lesson 3-4: Polygons

6. Find the measure of each interior angle using the given information.B A
(2x + 15)°
(3x - 20)° x°
(x + 15)° C D
Lesson 3-4: Polygons

7. Sum of the Exterior Angles =
60°
90°
90°
60°
60°
90°
90°
100°
100°
108°
108°
108°
80°
80°
108°
108°
Lesson 3-4: Polygons

8. Convex Polygon Formulas…..
For a convex polygon with n sides:
The sum of the interior angles is
The sum of the exterior angles is
The measure of one exterior angle is
The measure of exterior angle + interior angle is
Lesson 3-4: Polygons

9. Find the measure of the interior and exterior angle of each regular polygon.
A) 30-gon
Exterior Angle =
Interior Angle =
B) Pentagon
C) 14-gon
Lesson 3-4: Polygons

10. The measure of an interior angle of a regular polygon is given
The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon.
A) 144
B) 156
Lesson 3-4: Polygons