Title: ANGLES OF POLYGONS
1ANGLES OF POLYGONS
JIM SMITH JCHS
2POLYGONS
NOT POLYGONS
3CONCAVE
CONVEX
TRY THE PEGBOARD AND RUBBER BAND TEST
4NAMES 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
5INTERIOR ANGLE SUM OF CONVEX POLYGONS
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS
FROM ONE VERTEX
6 SIDES 4 TRIANGLES
6INTERIOR ANGLE SUM
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS
FROM ONE VERTEX
4 SIDES 2 TRIANGLES
7INTERIOR ANGLE SUM
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS
FROM ONE VERTEX
8 SIDES
6 TRIANGLES
8INTERIOR ANGLE SUM
- EACH TRIANGLE HAS 180
- IF N IS THE NUMBER OF SIDES THEN
- INT ANGLE SUM
- (N 2 ) 180
92
3
1
4
5
INT ANGLE SUM ( 5 2 ) 180
( 3 ) 180 540
10REGULAR POLYGONS
- REGULAR POLYGONS HAVE EQUAL SIDES AND EQUAL
ANGLES SO WE CAN FIND THE MEASURE OF EACH
INTERIOR ANGLE
11EACH INTERIOR ANGLE OF A REGULAR POLYGON
(N 2 ) 180 N
REMEMBER N NUMBER OF SIDES
12REGULAR HEXAGON
INT ANGLE SUM (6 2 ) 180 720
EACH INT ANGLE 720 120 6
13EXTERIOR 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
14NAME ____________ SIDES ____8________ INT
ANGLE SUM _________ EACH INT ANGLE
_________ EXT ANGLE SUM _________ EACH EXT
ANGLE _________
15NAME 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
16NAME DECAGON SIDES ____________ INT ANGLE
SUM _________ EACH INT ANGLE _________ EXT
ANGLE SUM _________ EACH EXT ANGLE
_________
17NAME 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
18NAME ____________ SIDES ____________ INT
ANGLE SUM _________ EACH INT ANGLE
_________ EXT ANGLE SUM _________ EACH EXT
ANGLE 60______
19NAME 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