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# 10 2 diagonals and angle measure

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• ON A PEGBOARD, A RUBBER BAND WILL COPY THE CONVEX SHAPE
• ### 10 2 diagonals and angle measure

1. 1. ANGLESANGLES OFOFPOLYGONSPOLYGONSSECTION 10-2SECTION 10-2JIM SMITH JCHS
2. 2. POLYGONSNOT POLYGONS
3. 3. CONCAVECONVEXTRY THE PEGBOARD AND RUBBER BAND TEST
4. 4. NAMES OF POLYGONSNAMES OF POLYGONSSIDESSIDESTRIANGLE 3TRIANGLE 3QUADRILATERAL 4QUADRILATERAL 4PENTAGON 5PENTAGON 5HEXAGON 6HEXAGON 6HEPTAGON 7HEPTAGON 7OCTAGON 8OCTAGON 8NONAGON 9NONAGON 9DECAGON 10DECAGON 10DODECAGON 12DODECAGON 12N – GON NN – GON NSEE PAGE 46 IN TEXTBOOK
5. 5. INTERIOR ANGLE SUMOF CONVEX POLYGONSFIND THE NUMBEROF TRIANGLESFORMED BYDIAGONALS FROMONE VERTEX6 SIDES = 4 TRIANGLES
6. 6. INTERIOR ANGLE SUMFIND THE NUMBEROF TRIANGLESFORMED BYDIAGONALS FROMONE VERTEX4 SIDES = 2 TRIANGLES
7. 7. INTERIOR ANGLE SUMFIND THE NUMBEROF TRIANGLESFORMED BYDIAGONALS FROMONE VERTEX8 SIDES = 6 TRIANGLES
8. 8. INTERIOR ANGLE SUMEACH TRIANGLE HAS 180°EACH TRIANGLE HAS 180°IF N IS THE NUMBER OF SIDESIF N IS THE NUMBER OF SIDESTHEN:THEN:INT ANGLE SUM =INT ANGLE SUM =(N – 2 ) 180°(N – 2 ) 180°
9. 9. 12345INT ANGLE SUM = ( 5 – 2 ) 180°( 3 ) 180° = 540°
10. 10. REGULAR POLYGONSREGULAR POLYGONSREGULAR POLYGONSREGULAR POLYGONSHAVE EQUAL SIDES ANDHAVE EQUAL SIDES ANDEQUAL ANGLES SO WEEQUAL ANGLES SO WECAN FIND THE MEASURECAN FIND THE MEASUREOFOF EACHEACH INTERIOR ANGLEINTERIOR ANGLE
11. 11. EACH INTERIOR ANGLE OFA REGULAR POLYGON =(N – 2 ) 180(N – 2 ) 180NNREMEMBER N = NUMBER OF SIDES
12. 12. REGULAR HEXAGONREGULAR HEXAGONINT ANGLE SUM =INT ANGLE SUM =(6 – 2 ) 180 =(6 – 2 ) 180 = 720720°°EACH INT ANGLE =EACH INT ANGLE =720720 == 120120°°66
13. 13. ALL POLYGONSALL POLYGONSHAVE ANHAVE AN EXTERIOREXTERIORANGLE SUMANGLE SUM OFOF360°360°EXTERIOR ANGLEEXTERIOR ANGLEEXTERIOR ANGLE SUMTHE MEASURE OF EACH EXTERIORANGLE OF A REGULAR POLYGON IS360°N
14. 14. NAME ____________NAME ____________# SIDES ____# SIDES ____ 88________________INT ANGLE SUMINT ANGLE SUM__________________EACH INT ANGLEEACH INT ANGLE__________________EXT ANGLE SUMEXT ANGLE SUM__________________EACH EXT ANGLEEACH EXT ANGLE__________________
15. 15. NAMENAME OctagonOctagon# SIDES ____# SIDES ____ 88________________INT ANGLE SUMINT ANGLE SUM 6 x 180 =6 x 180 =1080°1080°EACH INT ANGLEEACH INT ANGLE 1080 / 8 =1080 / 8 =135°135° EXT ANGLE SUMEXT ANGLE SUM 360°360°
16. 16. NAMENAME DECAGONDECAGON# SIDES ____________# SIDES ____________INT ANGLE SUMINT ANGLE SUM__________________EACH INT ANGLEEACH INT ANGLE__________________EXT ANGLE SUMEXT ANGLE SUM__________________EACH EXT ANGLEEACH EXT ANGLE__________________
17. 17. NAMENAME DECAGONDECAGON# SIDES# SIDES 1010INT ANGLE SUMINT ANGLE SUM 8 x 180 =8 x 180 =1440°1440°EACH INT ANGLEEACH INT ANGLE 1440 / 10 =1440 / 10 =144°144°EXT ANGLE SUMEXT ANGLE SUM 360°360°
18. 18. NAME ____________NAME ____________# SIDES ____________# SIDES ____________INT ANGLE SUMINT ANGLE SUM__________________EACH INT ANGLEEACH INT ANGLE__________________EXT ANGLE SUMEXT ANGLE SUM__________________EACH EXT ANGLEEACH EXT ANGLE60______60______
19. 19. NAMENAME HEXAGONHEXAGON# SIDES# SIDES 360 / 60 =360 / 60 = 66INT ANGLE SUMINT ANGLE SUM (6-2) X 180 =(6-2) X 180 =720°720°EACH INT ANGLEEACH INT ANGLE 720 / 6 =720 / 6 =120°120°EXT ANGLE SUMEXT ANGLE SUM 360°360°