Notes on 6-1,6-2

1. ANGLES OF
POLYGONS
SECTION 6-1, 1-6
JIM SMITH JCHS
3108.4.10
3108.4.12

2. POLYGONS
NOT POLYGONS

3. CONCAVE
CONVEX
TRY THE PEGBOARD AND RUBBER BAND TEST

4. NAMES OF POLYGONS
SIDES
TRIANGLE 3
QUADRILATERAL 4
PENTAGON 5
HEXAGON 6
HEPTAGON 7
OCTAGON 8
NONAGON 9
DECAGON 10
DODECAGON 12
N – GON N
SEE PAGE 390 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°
IF N IS THE NUMBER OF SIDES
THEN:
INT ANGLE SUM =
(N – 2 ) 180°

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

10. REGULAR POLYGONS
REGULAR POLYGONS
HAVE EQUAL SIDES AND
EQUAL ANGLES SO WE
CAN FIND THE MEASURE
OF EACH INTERIOR ANGLE

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

12. REGULAR HEXAGON
INT ANGLE SUM =
(6 – 2 ) 180 = 720°
EACH INT ANGLE =
720 = 120°
6

13. ALL POLYGONS
HAVE AN EXTERIOR
ANGLE SUM OF
360°
EXTERIOR ANGLE
EXTERIOR ANGLE SUM
THE MEASURE OF EACH EXTERIOR
ANGLE OF A REGULAR POLYGON IS
360°
N

14. NAME ____________
# SIDES ____8________
INT ANGLE SUM _________
EACH INT ANGLE _________
EXT ANGLE SUM _________
EACH EXT ANGLE _________

15. NAME Octagon
# SIDES ____8________
INT ANGLE SUM 6 x 180 = 1080°
EACH INT ANGLE 1080 / 8 = 135°
EXT ANGLE SUM 360°
EACH EXT ANGLE 360 / 8 = 45°

16. NAME DECAGON
# SIDES ____________
INT ANGLE SUM _________
EACH INT ANGLE _________
EXT ANGLE SUM _________
EACH EXT ANGLE _________

17. NAME DECAGON
# SIDES 10
INT ANGLE SUM 8 x 180 = 1440°
EACH INT ANGLE 1440 / 10 = 144°
EXT ANGLE SUM 360°
EACH EXT ANGLE 360 / 10 = 36°

18. NAME ____________
# SIDES ____________
INT ANGLE SUM _________
EACH INT ANGLE _________
EXT ANGLE SUM _________
EACH EXT ANGLE 60______

19. NAME HEXAGON
# SIDES 360 / 60 = 6
INT ANGLE SUM (6-2) X 180 = 720°
EACH INT ANGLE 720 / 6 = 120°
EXT ANGLE SUM 360°
EACH EXT ANGLE 60