ANGLES OF POLYGONS SECTION 8-1 JIM SMITH JCHS

POLYGONS NOT POLYGONS

CONCAVE CONVEX TRY THE PEGBOARD AND RUBBER BAND TEST

NAMES OF POLYGONS SIDES 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

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° IF N IS THE NUMBER OF SIDES THEN: INT ANGLE SUM = (N – 2 ) 180°

INT ANGLE SUM = ( 5 – 2 ) 180° ( 3 ) 180° = 540°

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

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

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

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°

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

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°

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

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