Problem: What is the degree measure of each interior angle and exterior angle in a regular 18-gon? 18-gon: polygon with 18 sides regular: all angles are.

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Presentation transcript:

Problem: What is the degree measure of each interior angle and exterior angle in a regular 18-gon? 18-gon: polygon with 18 sides regular: all angles are equal all sides are equal

Process: Need to know formula/pattern for total angle measures INSIDE polygons. Need to know formula/pattern for total angle measures OUTSIDE polygons Need to divide the total by 18

What I already know: The total number of degrees in a 3-sided polygon (triangle) is 180 Linear pair = 180°

Tips (Interior Angle Groups) Divide the polygon into triangles and cut them out Knowing what you already know about the angles in a triangle, determine the sum of the angles in the pentagon Look for a patter or formula

Tips (Exterior Angle Groups) Determine the sum of the INTERIOR angles first

1. I think the total number of degrees INSIDE/OUTSIDE a pentagon is: 2. I think the rule for any polygon is: 3. Using this the rule the measure of each INTERIOR/EXTERIOR angle in an 18-gon is:

Polygons

Define vocabulary need to discuss polygons; find formulas for the sum of the interior and exterior angles in any polygon and use them to find angle measures in regular polygons How is the sum of the interior angles of a polygon determined? What is true about the sum of the exterior angles of any polygon?

Polygons Closed figures No curves Sides meet end point to end point

Diagonal: a segment connecting two vertices in a polygon.

Types of Polygons Concave: diagonals can go outside the polygon Convex:

Equiangular Polygon Equilateral Polygon all angles are equal all sides are equal Regular Polygon all sides & angles are equal in measure.

Names of Polygons Triangle: 3 sides Octagon: 8 sides Quadrilateral: 4 sides Nonagon: 9 sides Pentagon: 5 sides Decagon: 10 sides Hexagon: 6 sides Undecagon: 11 sides Heptagon: 7 sides Dodecagon: 12 sides

Theorems Total of Interior Angles: 180n – 360 Total of Exterior Angles = 360° # of sides

Practice Find the total sum of the interior angles in a… 1. Octagon 2. Heptagon

Practice Find the measure of each angle in a REGULAR 3. Nonagon 4. Decagon

Practice Find the missing angle in each figure 1. 2.