1. Determine the name of the polygon
1) 4 sides
Quadrilateral
2) 6 sides
Hexagon
3) 7 sides
Heptagon
4) sides
Decagon
Determine if the polygon is convex or concave. 5)
Convex 6)
Concave

2. 16.02 Interior Angle Sum of a Polygon

3. Notice: The 4 sided figure (quadrilateral) into two triangles.
A diagonal is a line segment that joins any two non-consecutive vertices.
Examples of a Diagonal A B C D
Notice: The 4 sided figure (quadrilateral) into two triangles.

4. Draw the diagonals from vertex A.B H C
Notice: The 8 sided figure (octagon) into six triangles. D G F E
The number of triangles will always be two less than the number of sides. ( n – 2 )
The number of diagonals drawn from any vertex in the polygon will always be three less than the number of sides. ( n – 3 )

5. Interior Angle Sum = ( n – 2 )( 180° )
Find E B
To find the interior angle sum, draw all the diagonals from Vertex A. D C
Each triangle has a sum of 180°.
3 ● 180° = 540°.
A rule can be found using this idea.
Interior Angle Sum = ( # of triangles)( 180° )
Interior Angle Sum = ( n – 2 )( 180° )

6. Interior Angle Sum = ( n – 2 )( 180° )
Find the interior angle sum of each polygon.
( n – 2 ) • 180°
( 4 – 2 ) • 180°
( 2 ) • 180°
360°
( n – 2 ) • 180°
( 8 – 2 ) • 180°
( 6 ) • 180°
1080°

7. Interior Angle Sum = ( n – 2 )( 180° )
Find the interior angle sum of each polygon.
Heptagon
( 7 – 2 ) • 180°
( 5 ) • 180°
900°
Dodecagon
( 12 – 2 ) • 180°
( 10 ) • 180°
1800°

8. 120° 144° Find the measure of one interior angle. ( 6 – 2 ) • 180°
If the polygon is regular, one can find the measure of one interior angle by finding the angle sum and dividing by the number of interior angles.
Find the measure of one interior angle.
( 6 – 2 ) • 180°
720° ÷ 6
( 4 ) • 180°
120°
720°
Decagon
( 10 – 2 ) • 180°
1440° ÷ 10
( 8 ) • 180°
144°
1440°