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# 8 1 angles of polygons

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• ON A PEGBOARD, A RUBBER BAND WILL COPY THE CONVEX SHAPE
• ### 8 1 angles of polygons

1. 1. ANGLES OF POLYGONS SECTION 8-1 JIM SMITH JCHS
2. 2. POLYGONS NOT POLYGONS
3. 3. CONCAVE CONVEX TRY THE PEGBOARD AND RUBBER BAND TEST
4. 4. NAMES OF POLYGONS <ul><li>SIDES </li></ul><ul><li>TRIANGLE 3 </li></ul><ul><li>QUADRILATERAL 4 </li></ul><ul><li>PENTAGON 5 </li></ul><ul><li>HEXAGON 6 </li></ul><ul><li>HEPTAGON 7 </li></ul><ul><li>OCTAGON 8 </li></ul><ul><li>NONAGON 9 </li></ul><ul><li>DECAGON 10 </li></ul><ul><li>DODECAGON 12 </li></ul><ul><li>N – GON N </li></ul>SEE PAGE 46 IN TEXTBOOK
5. 5. INTERIOR ANGLE SUM OF CONVEX POLYGONS FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 6 SIDES = 4 TRIANGLES
6. 6. INTERIOR ANGLE SUM FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 4 SIDES = 2 TRIANGLES
7. 7. INTERIOR ANGLE SUM FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX 8 SIDES = 6 TRIANGLES
8. 8. INTERIOR ANGLE SUM <ul><li>EACH TRIANGLE HAS 180° </li></ul><ul><li>IF N IS THE NUMBER OF SIDES THEN: </li></ul><ul><li>INT ANGLE SUM = </li></ul><ul><li>(N – 2 ) 180° </li></ul>
9. 9. 1 2 3 4 5 INT ANGLE SUM = ( 5 – 2 ) 180 ° ( 3 ) 180 ° = 540 °
10. 10. REGULAR POLYGONS <ul><li>REGULAR POLYGONS HAVE EQUAL SIDES AND EQUAL ANGLES SO WE CAN FIND THE MEASURE OF EACH INTERIOR ANGLE </li></ul>
11. 11. EACH INTERIOR ANGLE OF A REGULAR POLYGON = (N – 2 ) 180 N REMEMBER N = NUMBER OF SIDES
12. 12. REGULAR HEXAGON INT ANGLE SUM = (6 – 2 ) 180 = 720 ° EACH INT ANGLE = 720 = 120 ° 6
13. 13. ALL POLYGONS HAVE AN EXTERIOR ANGLE SUM OF 360° EXTERIOR ANGLE EXTERIOR ANGLE SUM THE MEASURE OF EACH EXTERIOR ANGLE OF A REGULAR POLYGON IS 360° N
14. 14. NAME ____________ # SIDES ____ 8 ________ INT ANGLE SUM _________ EACH INT ANGLE _________ EXT ANGLE SUM _________ EACH EXT ANGLE _________
15. 15. 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°
16. 16. NAME DECAGON # SIDES ____________ INT ANGLE SUM _________ EACH INT ANGLE _________ EXT ANGLE SUM _________ EACH EXT ANGLE _________
17. 17. 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°
18. 18. NAME ____________ # SIDES ____________ INT ANGLE SUM _________ EACH INT ANGLE _________ EXT ANGLE SUM _________ EACH EXT ANGLE 60______
19. 19. 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