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8.1 Angle Measures in Polygons

8.1 Angle Measures in Polygons. Sum of measures of interior angles. # of triangles. # of sides. 1(180)=180. 3. 1. 2(180)=360. 4. 2. 3. 3(180)=540. 5. 6. 4. 4(180)=720. n-2. (n-2) • 180. n.

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8.1 Angle Measures in Polygons

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  1. 8.1 Angle Measures in Polygons

  2. Sum of measures of interior angles # of triangles # of sides 1(180)=180 3 1 2(180)=360 4 2 3 3(180)=540 5 6 4 4(180)=720 n-2 (n-2) • 180 n

  3. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

  4. If a regular convex polygon has n sides, then the measure of one of the interior angles is

  5. Ex. 1 Use a regular 15-gon to answer the questions. • Find the sum of the measures of the interior angles. • Find the measure of ONE interior angle 2340° 156°

  6. Ex: 2 Find the value of x in the polygon x 126 100 143 130 117 126 + 130 + 117 + 143 + 100 + x = 720 616 + x = 720 x = 104

  7. Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have? One interior angle A regular dodecagon

  8. Interior Angles Exterior Angles Two more important terms

  9. 2 1 3 5 4 The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°.

  10. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°. 1 3 2

  11. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°. 1 2 4 3

  12. The measure of each exterior angle of a regular polygon is

  13. Ex. 4 Find the measure of ONE exterior angle of a regular 20-gon. 18°

  14. Ex. 5 Find the measure of ONE exterior angle of a regular heptagon. 51.4°

  15. Ex. 6 The sum of the measures of five interior angles of a hexagon is 625. What is the measure of the sixth angle? 95°

  16. Find the measure of an interior angle and an exterior angle for the indicated regular polygon • Regular 18-gon • Interior Angles • (n-2)*180 = 2880 • 2880/18 = 160 • Exterior Angles • 180 – 160 = 20

  17. Let’s practice! Classwork/homework

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