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TechMathI - 5.2 - Angles of Polygons

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TechMathI - 5.2 - Angles of Polygons

1. 1. Bell Ringer<br />1. Name all diagonals with an endpoint at vertex B.<br />2. Name all angles not adjacent to D.<br />3. Name the polygon.<br />2x + 2<br />The perimeter of the parallelogram is 84 feet. 4. Find the length of the base.<br />4x - 2<br />
2. 2. Polygon Interior Angles Theorem<br />- the sum of the measures of the interior angles of a polygon with n sides is (n – 2)(180°)<br />
3. 3. Find the sum of the measures of the interior angles.<br />7 sides<br />10 sides<br />11 sides<br />9 sides<br />12 sides<br />16 sides<br />20 sides<br />
4. 4. Polygon Exterior Angles Theorem<br />- the sum of the measures of the exterior angles, one at each vertex is 360°<br />
5. 5. Interior Angles<br />Exterior Angles<br />?<br />Exterior Angles of Polygons<br />180o<br />Exterior angles of a polygon sum to 360o.<br />
6. 6. 72o<br />90o<br />108o<br />120o<br />72o<br />90o<br />90o<br />90o<br />60o<br />108o<br />108o<br />Square<br />Pentagon<br />72o<br />3<br />4<br />5<br />108o<br />72o<br />120o<br />108o<br />90o<br />90o<br />90o<br />60o<br />60o<br />120o<br />90o<br />72o<br />Equilateral Triangle<br />45o<br />60o<br />45o<br />45o<br />60o<br />60o<br />Octagon<br />Hexagon<br />45o<br />45o<br />6<br />8<br />60o<br />60o<br />45o<br />45o<br />60o<br />45o<br />Exterior Angles of Polygons<br />Regular Polygons<br />Interior angles are 180 – 45 = 135o<br />Interior angles are 180 – 60 = 120o<br />
7. 7. Calculate the exterior and interior angles of each of these regular polygons.<br />2<br />4<br />3<br />1<br />7 sides<br />10 sides<br />11 sides<br />9 sides<br />6<br />7<br />5<br />12 sides<br />16 sides<br />20 sides<br />Exterior Angles of Polygons<br />Septagon/Heptagon<br />Decagon<br />Hendecagon<br />Nonagon<br />51.4o/128.6o<br />40o/140o<br />36o/144o<br />32.7o/147.3o<br />Icosagon<br />Hexadecagon<br />Dodecagon<br />18o/162o<br />22.5o/157.5o<br />30o/150o<br />
8. 8. Diagrams not accurately drawn<br />Exterior Angles of Polygons<br />Calculate the value of the unknown angles.<br />2<br />1<br />88o<br />x<br />125o<br />115o<br />w<br />108o<br />z<br />80o<br />4<br />55o<br />3<br />?<br />125o<br />45o<br />70o<br />65o<br />58o<br />32o<br />y<br />?<br />Angle w = 360 – (125 + 90) = 145o<br />Angle x = 360 – (108 + 88 + 115) = 49o<br />55o<br />122o<br />Angle z = 360 – (32 + 70 + 55 + 45 + 122) = 36o<br />Angle y = 360 – (90 + 55 + 80 + 65) = 70o<br />
9. 9. Diagrams not accurately drawn<br />You try!<br />1<br />2<br />110o<br />110o<br />x<br />w<br />85o<br />130o<br />z<br />y<br />4<br />63o<br />3<br />45o<br />55o<br />33o<br />115o<br />130o<br />58o<br />73o<br />
10. 10. What’s happened? (mathematically speaking)<br />And finally:<br />A hendecagon is laying eggsagons!<br />