This document discusses properties of polygons, including: - The names of common polygons based on their number of sides. - A formula to calculate the interior angle sum of any polygon as (n-2) * 180 degrees, where n is the number of sides. - Methods for finding the number of triangles formed by diagonals from one vertex of a polygon. - Formulas for calculating properties of regular polygons like interior angle measurements and exterior angle measurements.

1. ANGLESANGLES OFOF
POLYGONSPOLYGONS
SECTION 10-2SECTION 10-2
JIM SMITH JCHS

2. POLYGONS
NOT POLYGONS

3. CONCAVE
CONVEX
TRY THE PEGBOARD AND RUBBER BAND TEST

4. NAMES OF POLYGONSNAMES OF POLYGONS
SIDESSIDES
TRIANGLE 3TRIANGLE 3
QUADRILATERAL 4QUADRILATERAL 4
PENTAGON 5PENTAGON 5
HEXAGON 6HEXAGON 6
HEPTAGON 7HEPTAGON 7
OCTAGON 8OCTAGON 8
NONAGON 9NONAGON 9
DECAGON 10DECAGON 10
DODECAGON 12DODECAGON 12
N – GON NN – GON N
SEE PAGE 46 IN TEXTBOOK

5. INTERIOR ANGLE SUM
OF CONVEX POLYGONS
FIND THE NUMBER
OF TRIANGLES
FORMED BY
DIAGONALS FROM
ONE VERTEX
6 SIDES = 4 TRIANGLES

6. INTERIOR ANGLE SUM
FIND THE NUMBER
OF TRIANGLES
FORMED BY
DIAGONALS FROM
ONE VERTEX
4 SIDES = 2 TRIANGLES

7. INTERIOR ANGLE SUM
FIND THE NUMBER
OF TRIANGLES
FORMED BY
DIAGONALS FROM
ONE VERTEX
8 SIDES = 6 TRIANGLES

8. INTERIOR ANGLE SUM
EACH TRIANGLE HAS 180°EACH TRIANGLE HAS 180°
IF N IS THE NUMBER OF SIDESIF N IS THE NUMBER OF SIDES
THEN:THEN:
INT ANGLE SUM =INT ANGLE SUM =
(N – 2 ) 180°(N – 2 ) 180°

9. 1
2
3
4
5
INT ANGLE SUM = ( 5 – 2 ) 180°
( 3 ) 180° = 540°

10. REGULAR POLYGONSREGULAR POLYGONS
REGULAR POLYGONSREGULAR POLYGONS
HAVE EQUAL SIDES ANDHAVE EQUAL SIDES AND
EQUAL ANGLES SO WEEQUAL ANGLES SO WE
CAN FIND THE MEASURECAN FIND THE MEASURE
OFOF EACHEACH INTERIOR ANGLEINTERIOR ANGLE

11. EACH INTERIOR ANGLE OF
A REGULAR POLYGON =
(N – 2 ) 180(N – 2 ) 180
NN
REMEMBER N = NUMBER OF SIDES

12. REGULAR HEXAGONREGULAR HEXAGON
INT ANGLE SUM =INT ANGLE SUM =
(6 – 2 ) 180 =(6 – 2 ) 180 = 720720°°
EACH INT ANGLE =EACH INT ANGLE =
720720 == 120120°°
66

13. ALL POLYGONSALL POLYGONS
HAVE ANHAVE AN EXTERIOREXTERIOR
ANGLE SUMANGLE SUM OFOF
360°360°
EXTERIOR ANGLEEXTERIOR ANGLE
EXTERIOR ANGLE SUM
THE MEASURE OF EACH EXTERIOR
ANGLE OF A REGULAR POLYGON IS
360°
N

14. NAME ____________NAME ____________
# SIDES ____# SIDES ____ 88________________
INT ANGLE SUMINT ANGLE SUM
__________________
EACH INT ANGLEEACH INT ANGLE
__________________
EXT ANGLE SUMEXT ANGLE SUM
__________________
EACH EXT ANGLEEACH EXT ANGLE
__________________

15. NAMENAME OctagonOctagon
# SIDES ____# SIDES ____ 88________________
INT ANGLE SUMINT ANGLE SUM 6 x 180 =6 x 180 =
1080°1080°
EACH INT ANGLEEACH INT ANGLE 1080 / 8 =1080 / 8 =
135°135° EXT ANGLE SUMEXT ANGLE SUM 360°360°

16. NAMENAME DECAGONDECAGON
# SIDES ____________# SIDES ____________
INT ANGLE SUMINT ANGLE SUM
__________________
EACH INT ANGLEEACH INT ANGLE
__________________
EXT ANGLE SUMEXT ANGLE SUM
__________________
EACH EXT ANGLEEACH EXT ANGLE
__________________

17. NAMENAME DECAGONDECAGON
# SIDES# SIDES 1010
INT ANGLE SUMINT ANGLE SUM 8 x 180 =8 x 180 =
1440°1440°
EACH INT ANGLEEACH INT ANGLE 1440 / 10 =1440 / 10 =
144°144°
EXT ANGLE SUMEXT ANGLE SUM 360°360°

18. NAME ____________NAME ____________
# SIDES ____________# SIDES ____________
INT ANGLE SUMINT ANGLE SUM
__________________
EACH INT ANGLEEACH INT ANGLE
__________________
EXT ANGLE SUMEXT ANGLE SUM
__________________
EACH EXT ANGLEEACH EXT ANGLE
60______60______

19. NAMENAME HEXAGONHEXAGON
# SIDES# SIDES 360 / 60 =360 / 60 = 66
INT ANGLE SUMINT ANGLE SUM (6-2) X 180 =(6-2) X 180 =
720°720°
EACH INT ANGLEEACH INT ANGLE 720 / 6 =720 / 6 =
120°120°
EXT ANGLE SUMEXT ANGLE SUM 360°360°