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Chapter 8.1 Notes: Find Angle Measures in Polygons

Chapter 8.1 Notes: Find Angle Measures in Polygons. Goal: You will find interior and exterior angle measures in polygons. Properties of a Polygon In a polygon, two vertices that are endpoints of the same side are called consecutive vertices .

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Chapter 8.1 Notes: Find Angle Measures in Polygons

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  1. Chapter 8.1 Notes: Find Angle Measures in Polygons Goal: You will find interior and exterior angle measures in polygons.

  2. 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.

  3. 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.

  4. 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.

  5. 1. 2. The coin shown is in the shape of a regular 11- gon. Find the sum of the measures of the interior angles. The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon by the number of sides. decagon ANSWER ANSWER 1620° for Examples 1 and 2 GUIDED PRACTICE

  6. 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.

  7. 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.

  8. 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.

  9. 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°.

  10. 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?

  11. 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.

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