ANGLES OF POLYGONS

1
ANGLES OF POLYGONS

• SECTION 8-1

JIM SMITH JCHS
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 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
• IF N IS THE NUMBER OF SIDES THEN
• INT ANGLE SUM
• (N 2 ) 180

9
2
3
1
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
EXTERIOR ANGLE SUM
EXTERIOR ANGLE
THE MEASURE OF EACH EXTERIOR ANGLE OF A REGULAR
POLYGON IS 360 N
ALL POLYGONS HAVE AN EXTERIOR ANGLE SUM OF
360
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