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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

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• 1. ANGLESANGLES OFOFPOLYGONSPOLYGONSSECTION 10-2SECTION 10-2JIM SMITH JCHS
• 2. POLYGONSNOT POLYGONS
• 3. CONCAVECONVEXTRY THE PEGBOARD AND RUBBER BAND TEST
• 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. INTERIOR ANGLE SUMOF CONVEX POLYGONSFIND THE NUMBEROF TRIANGLESFORMED BYDIAGONALS FROMONE VERTEX6 SIDES = 4 TRIANGLES
• 6. INTERIOR ANGLE SUMFIND THE NUMBEROF TRIANGLESFORMED BYDIAGONALS FROMONE VERTEX4 SIDES = 2 TRIANGLES
• 7. INTERIOR ANGLE SUMFIND THE NUMBEROF TRIANGLESFORMED BYDIAGONALS FROMONE VERTEX8 SIDES = 6 TRIANGLES
• 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. 12345INT ANGLE SUM = ( 5 – 2 ) 180°( 3 ) 180° = 540°
• 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. EACH INTERIOR ANGLE OFA REGULAR POLYGON =(N – 2 ) 180(N – 2 ) 180NNREMEMBER N = NUMBER OF SIDES
• 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. 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. 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. 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. 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. 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. 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. 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°