ANGLES OF
POLYGONS
SPI 3108.4.3
Identify, describe and/or apply the relationships
and theorems involving different types of
triangles, quadrilaterals and other polygons.
JIM SMITH JCHS
POLYGONS
NOT POLYGONS
CONCAVE
CONVEX
TRY THE PEGBOARD AND RUBBER BAND TEST
NAMES OF POLYGONS
SIDES
TRIANGLE 3
QUADRILATERAL 4
PENTAGON 5
HEXAGON 6
HEPTAGON 7
OCTAGON 8
NONAGON 9
DECAGON 10
SEE PAGE 46 IN TEXTBOOK
DODECAGON 12
N – GON N
INTERIOR ANGLE SUM
OF CONVEX POLYGONS
FIND THE NUMBER
OF TRIANGLES
FORMED BY
DIAGONALS FROM
ONE VERTEX
6 SIDES = 4 TRIANGLES
INTERIOR ANGLE SUM
FIND THE NUMBER
OF TRIANGLES
FORMED BY
DIAGONALS FROM
ONE VERTEX
4 SIDES = 2 TRIANGLES
INTERIOR ANGLE SUM
FIND THE NUMBER
OF TRIANGLES
FORMED BY
DIAGONALS FROM
ONE VERTEX
8 SIDES = 6 TRIANGLES
INTERIOR ANGLE SUM
EACH TRIANGLE HAS 180
DEGREES
IF N IS THE NUMBER OF SIDES
THEN:
(N – 2 ) 180 = INT ANGLE
SUM
2
3
1
4
5
INT ANGLE SUM = ( 5 – 2 ) 180
( 3 ) 180 = 540 DEGREES
REGULAR POLYGONS
REGULAR POLYGONS
HAVE EQUAL SIDES AND
EQUAL ANGLES SO WE
CAN FIND THE MEASURE
OF EACH INTERIOR ANGLE
EACH INTERIOR ANGLE OF
A REGULAR POLYGON =
(N – 2 ) 180
N
REMEMBER N = NUMBER OF SIDES
REGULAR HEXAGON
INT ANGLE SUM =
(6 – 2 ) 180 = 720
EACH INT ANGLE =
720 = 120
6
EXTERIOR ANGLE SUM
EXTERIOR ANGLE
ALL POLYGONS THE MEASURE OF EACH EXTERIOR
HAVE AN EXTERIOR ANGLE OF A REGULAR POLYGON
ANGLE SUM OF IS 360
360 N