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Polygons and Quadrilaterals
©Tentinger
 How many sides do a pentagon, hexagon, and

heptagon have?
 What conjecture can you make about the sum of the
interior angles of each figure?
Angle Sum Theorem
 The sum of the measures of the interior angles of an

n-gon is (n – 2)180
 What is the measure of <G?

 What is the measure of <Y?
Polygon Exterior Angle Theorem
 The sum of the measures of the exterior angles of a

polygon, one at each vertex, is 360
 <1 + <2 + <3 + <4 + <5 = 360
 What is the measure of an exterior angle

of a regular 18-gon?
 What is the sum of measures of a polygon with 180

sides?
Homework
 Pg. 161
 #11 – 25, 40 – 44, 47 – 49
 23 problems

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Angle Sum Theorem

  • 2.  How many sides do a pentagon, hexagon, and heptagon have?  What conjecture can you make about the sum of the interior angles of each figure?
  • 3. Angle Sum Theorem  The sum of the measures of the interior angles of an n-gon is (n – 2)180  What is the measure of <G?  What is the measure of <Y?
  • 4.
  • 5. Polygon Exterior Angle Theorem  The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360  <1 + <2 + <3 + <4 + <5 = 360
  • 6.
  • 7.  What is the measure of an exterior angle of a regular 18-gon?  What is the sum of measures of a polygon with 180 sides?
  • 8. Homework  Pg. 161  #11 – 25, 40 – 44, 47 – 49  23 problems