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Interior and Exterior Angles

Interior and Exterior Angles. Slideshow 34, Mathematics Mr Richard Sasaki, Room 307. Objectives. Recall and learn the sum of interior angles in certain polygons and their names Understand the meaning of “exterior angle” and how to calculate them. Shape names and interior angles. 540 o.

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Interior and Exterior Angles

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  1. Interior and Exterior Angles Slideshow 34, Mathematics Mr Richard Sasaki, Room 307

  2. Objectives • Recall and learn the sum of interior angles in certain polygons and their names • Understand the meaning of “exterior angle” and how to calculate them

  3. Shape names and interior angles 540o 180o 360o 720o Triangle Pentagon Quadrilateral Hexagon 1260o 900o 1080o 1440o Decagon Nonagon Septagon / Heptagon Octagon 1800o 1620o Hendecagon / Undecagon Dodecagon

  4. Shape names and interior angles A regular shape is a shape that has all edges the same length. All angles are also the same. Some regular shapes have special names. What do we call a regular triangle? An Equilateral Triangle What do we call a regular quadrilateral? A square. (A rectangle has two pairs of common lengths but equal angles.)

  5. Calculating angles With the properties of polygons that we have learned so far, we should be able to calculate a number of angles. All angles will add up to the sum of interior angles. (Of course!) Example Calculate each angle within a regular pentagon. = Angle = =

  6. Calculating angles We can also calculate angles in irregular shapes when one is missing (or two that are the same). Example Calculate the missing angle in the shape below. The shape has 4 sides so it’s a quadrilateral (360o). This is a right-angle, it’s 90o. 55o 140o

  7. Answers Easy Triangle – 60o Quadrilateral - 90o Pentagon - 108o Hexagon - 120o Heptagon – 900/7o Octagon - 135o Nonagon – 140o Decagon - 144o Undecagon – 1620/11o Dodecagon - 150o Hard 1. 85o 2. 61o 3. 10o 4. x = 32°; y = 122°; z = 58° 5. x = 70°; y = 55° 6. 86° 2. x=60o

  8. Exterior angles Exterior angles are angles outside of the polygon that connect with a line. Exterior angles must join with interior angles so that together, they make 1800. An exterior angle is always less than 180o. 108o 72o

  9. Exterior angles Next, complete the worksheet given and find out (or if you know, show) what the sum of exterior angles are for given polygons.

  10. Answers Hopefully you found out (or knew) that the sum of exterior angles is always equal to 360o!

  11. Useful notation Recall some useful notation when looking at shapes… What do the dashes mean? They imply that this pair of lines are the same length. Also, the angles shown must be the same! This shape is called an ________ triangle. isosceles

  12. Useful notation For the next notation… What do the arrows mean? They imply that this pair of lines are the parallel. They don’t imply the lines are the same length! This shape is called a _________. parallelogram

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