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Unit 3 Comp 4B

Unit 3 Comp 4B. Interior/Exterior Angles in Regular Polygons R.4.G.2 Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon interior and exterior angle measure of a regular polygon or irregular polygon

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Unit 3 Comp 4B

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  1. Unit 3 Comp 4B Interior/Exterior Angles in Regular Polygons R.4.G.2 Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon interior and exterior angle measure of a regular polygon or irregular polygon number of sides or angles of a polygon

  2. Definitions Regular Polygon: a polygon with all congruent sides and all congruent angles Diagonal: a line drawn through the interior of a polygon from a vertex to a non-consecutive vertex.

  3. Make a drawing of the indicated polygon. Then draw all diagonals from ONE vertex.

  4. How many triangles were formed?

  5. How many triangles were formed?

  6. Polygon Interior Angle Sum Theorem The sum of the measures of the interior angles of an n-gon is 180(n-2)

  7. Examples Find the sum of the interior angles of the following polygons: Dodecagon 18-gon

  8. Exterior Angles of Polygons • Draw an exterior angle at each vertex of the polygons. • Measure each exterior angle and find the sum of all the exterior angles for each polygon. Record your results in the table.

  9. Exterior Angles of Polygons

  10. Conclusion The sum of the exterior angles of any polygon is 360 degrees!

  11. More Conclusions To find one exterior angle of any polygon with “n” sides: Interior Angle + Exterior Angle = 180o

  12. Example Find the measure of each interior and exterior angle of a regular octagon. n = Exterior angle = Interior angle = 8 45o 135o

  13. Examples Find the measure of each interior and exterior angle of a 22-gon. Interior: 163.6o Exterior: 16.4o

  14. More Examples! If the exterior angle measures 40o in a regular polygon, how many sides does it have?

  15. So Many Examples! If the exterior angle measures 120o in a regular polygon, how many sides does it have?

  16. 55o xo xo 2xo (x+10)o yo xo (3x-17)o (x+10)o Last Page of Examples!

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