Warm-Up

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Warm-Up

• Sketch a convex quadrilateral, pentagon, and
  hexagon
• From ONE vertex draw all of the diagonals
• How many triangles did this create in each? Is
  there a relationship here?
• How could you use this to help you know the sum
  of the angles in a polygon?

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Section 6.1 The polygon angle sum theorem
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Theorem 6.1Polygon Angle Sums

• The sum of the measures of the interior angles of
  an n-gon is

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Example

• What is the sum of the interior angle measures of
  a heptagon?

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Try it on your own!

• What is the sum of the interior angle measures of
  a 17-gon?

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Example

• The common housefly, Musca domestica, has eyes
  that consist of approximately 400 facets. Each
  facet is a regular hexagon. What is the measure
  of each interior angle in the facet?

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Example

• What is mltY in pentagon TODAY?

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Try it on your own!

• What is mltG in quadrilateral EFGH?

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Exterior Angles

• http//www.regentsprep.org/regents/math/geometry/g
  g3/JavaExtAngles.htm
• Do you notice anything?

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Theorem 6.2 Exterior Angles of a Polygon

• The sum of the measures of the exterior angles of
  a polygon, one at each vertex, is 360 degrees.

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Example

• What is mlt1 in the regular octagon at the right?

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Try it on your own!

• What is the measure of an exterior angle of a
  regular nonagon?

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Homework

• P. 356 7-17, 18-24E, 27, 29-31