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TechMathI - 5.2 - Angles of Polygons
 

TechMathI - 5.2 - Angles of Polygons

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    TechMathI - 5.2 - Angles of Polygons TechMathI - 5.2 - Angles of Polygons Presentation Transcript

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