10 2 diagonals and angle measure

ANGLESANGLES OFOF POLYGONSPOLYGONS

SECTION 10-2SECTION 10-2

JIM SMITH JCHS

POLYGONS

NOT POLYGONS

CONCAVE

CONVEX

TRY THE PEGBOARD AND RUBBER BAND TEST

NAMES OF POLYGONSNAMES OF POLYGONS SIDES SIDES

TRIANGLE 3 TRIANGLE 3

QUADRILATERAL 4QUADRILATERAL 4

PENTAGON 5PENTAGON 5

HEXAGON 6HEXAGON 6

HEPTAGON 7HEPTAGON 7

OCTAGON 8OCTAGON 8

NONAGON 9NONAGON 9

DECAGON 10DECAGON 10

DODECAGON 12DODECAGON 12

N – GON NN – GON N

SEE PAGE 46 IN TEXTBOOK

INTERIOR ANGLE SUMOF CONVEX POLYGONS

FIND THE NUMBEROF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX

6 SIDES = 4 TRIANGLES

INTERIOR ANGLE SUM



INTERIOR ANGLE SUM

EACH TRIANGLE HAS 180°EACH TRIANGLE HAS 180°

IF N IS THE NUMBER OF SIDES IF N IS THE NUMBER OF SIDES THEN:THEN:

INT ANGLE SUM =INT ANGLE SUM =

(N – 2 ) 180°(N – 2 ) 180°

1

23

4

5

INT ANGLE SUM = ( 5 – 2 ) 180°

( 3 ) 180° = 540°

REGULAR POLYGONSREGULAR POLYGONS

REGULAR POLYGONSREGULAR POLYGONS HAVE EQUAL SIDES AND HAVE EQUAL SIDES AND EQUAL ANGLES SO WE EQUAL ANGLES SO WE

CAN FIND THE MEASURE CAN FIND THE MEASURE OF OF EACHEACH INTERIOR ANGLE INTERIOR ANGLE

EACH INTERIOR ANGLE OFA REGULAR POLYGON =

(N – 2 ) 180(N – 2 ) 180 NNREMEMBER N = NUMBER OF SIDES

REGULAR HEXAGONREGULAR HEXAGON

INT ANGLE SUM =INT ANGLE SUM =

(6 – 2 ) 180 =(6 – 2 ) 180 = 720720°°

EACH INT ANGLE = EACH INT ANGLE =

720720 = = 120120°° 66

ALL POLYGONSALL POLYGONS HAVE AN HAVE AN EXTERIOREXTERIOR ANGLE SUMANGLE SUM OF OF

360°360°

EXTERIOR ANGLEEXTERIOR ANGLE

EXTERIOR ANGLE SUM

THE MEASURE OF EACH EXTERIORANGLE OF A REGULAR POLYGON IS

360° N

NAME ____________NAME ____________# SIDES ____# SIDES ____88________________INT ANGLE SUM _________ INT ANGLE SUM _________ EACH INT ANGLE _________EACH INT ANGLE _________EXT ANGLE SUM _________EXT ANGLE SUM _________EACH EXT ANGLE _________EACH EXT ANGLE _________

NAME NAME OctagonOctagon

# SIDES ____# SIDES ____88________________

INT ANGLE SUM INT ANGLE SUM 6 x 180 =6 x 180 = 1080°1080°

EACH INT ANGLE EACH INT ANGLE 1080 / 8 =1080 / 8 = 135°135°

EXT ANGLE SUM EXT ANGLE SUM 360°360°

EACH EXT ANGLE EACH EXT ANGLE 360 / 8 =360 / 8 = 45°45°

NAME NAME DECAGONDECAGON# SIDES ____________# SIDES ____________INT ANGLE SUM _________ INT ANGLE SUM _________ EACH INT ANGLE _________EACH INT ANGLE _________EXT ANGLE SUM _________EXT ANGLE SUM _________EACH EXT ANGLE _________EACH EXT ANGLE _________

NAME NAME DECAGONDECAGON

# SIDES # SIDES 1010 INT ANGLE SUM INT ANGLE SUM 8 x 180 = 8 x 180 = 1440°1440° EACH INT ANGLE EACH INT ANGLE 1440 / 10 = 1440 / 10 = 144°144° EXT ANGLE SUM EXT ANGLE SUM 360°360°

EACH EXT ANGLE EACH EXT ANGLE 360 / 10 = 360 / 10 = 36°36°

NAME ____________NAME ____________# SIDES ____________# SIDES ____________INT ANGLE SUM _________ INT ANGLE SUM _________ EACH INT ANGLE _________EACH INT ANGLE _________EXT ANGLE SUM _________EXT ANGLE SUM _________EACH EXT ANGLE EACH EXT ANGLE 60______60______

NAME NAME HEXAGONHEXAGON

# SIDES # SIDES 360 / 60 = 360 / 60 = 66

INT ANGLE SUM INT ANGLE SUM (6-2) X 180 =(6-2) X 180 = 720°720°

EACH INT ANGLE EACH INT ANGLE 720 / 6 =720 / 6 = 120° 120°

EXT ANGLE SUM EXT ANGLE SUM 360°360°

EACH EXT ANGLE EACH EXT ANGLE 60 60

10 2 diagonals and angle measure

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