Angles of Polygons

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Section 6.2

• Angles of Polygons

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Theorem 6.1 Polygon Interior Angles Theorem

• The sum of the measures of the interior angles of
  a convex n-gon is
• (n-2)(180).

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Corollary to Theorem 6.1

• The measure of each interior angle of a regular
  n-gon is
• 1/n (n-2)(180)

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Theorem 6.2 Polygon Exterior Angles Theorem

• The sum of the measures of the exterior angles,
  one from each vertex, of a convex polygon is 360

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Corollary to Theorem 6.2

• The measure of each exterior angle of a regular
  n-gon is
• 1/n (360).

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Guided Practice

• What is the sum of the measures of the interior
  angles of a convex 12-sided polygon?
• What is the measure of each interior angle of a
  regular 20-sided polygon?

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3. A convex pentagon has interior angles that
measure 90, 100, 110, and 120. What is the
measure of the fifth interior angle?
4. A convex hexagon has exterior angle that
measure 32, 54, 67, 72 and 100. What is the
measure of the sixth exterior angle?
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5. What is the measure of each exterior angle of
a regular nonagon?
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Match the regular polygon with the measure of
each of its interior angles and exterior angles.
Interior angles a) 156 b) 144 c) 150
d) 135 e) 108 Exterior angles f) 36 g) 45
h) 30 i) 72 j) 24
6.regular pentagon 7.regular 12-gon
8.regular decagon 9.regular 15- gon 10.regular
octagon