Chapter 8.1 Notes: Find Angle Measures in Polygons

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Chapter 8.1 Notes Find Angle Measures in Polygons

• Goal You will find interior and exterior angle
  measures in polygons.

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• Properties of a Polygon
• In a polygon, two vertices that are endpoints of
  the same side are called consecutive vertices.
• A diagonal of a polygon is a segment that joins
  two nonconsecutive vertices.

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• Finding Interior Angle Measures in Polygons
• Theorem 8.1 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 8.1 Interior Angles of a
  Quadrilateral
• The sum of the measures of the interior angles
  of a quadrilateral is 360o.
• Ex.1 Find the sum of the measures of the
  interior angles of a convex octagon.

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for Examples 1 and 2
GUIDED PRACTICE
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• Ex.2 The sum of the measures of the interior
  angles of a convex polygon is 900o. Classify the
  polygon by the number of sides.
• Ex.3 Find the value of x in the diagram shown.

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• Ex.4 In the diagram below, find and
• Ex.5 The sum of the measures of the interior
  angles of a convex polygon is 1440o. Classify the
  polygon by the number of sides.

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• Finding Exterior Angle Measures in Polygons
• Theorem 8.2 Polygon Exterior Angles Theorem
• The sum of the measures of the exterior angles
  of a convex polygon, one angle at each vertex, is
  360o.

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Exterior Angle Sum Theorem

• Exterior Angle Sum TheoremIf a polygon is
  convex, then the sum of the measures of the
  exterior angles, one at each vertex, is 360.

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• Ex.6 What is the value of x in the diagram
  shown?
• Ex.7 A convex hexagon has exterior angles with
  measures 34o, 49o, 58o, 67o, and 75o. What is the
  measure of an exterior angle at the sixth vertex?
  

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• Ex.8 The trampoline shown is shaped like a
  regular dodecagon. Find (a) the measure of each
  interior angle, and (b) the measure of each
  exterior angle.
• Ex.9 A stop sign is shaped like a regular
  octagon. Find (a) the measure of each interior
  angle, and (b ) the measure of each exterior
  angle.