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8.1 – Find Angle Measures in Polygons

8.1 – Find Angle Measures in Polygons. Angle inside a shape. 2. 1. 2. Angle outside a shape. 1. Line connecting two nonconsecutive vertices. triangle. 1. 180 °. 2. 360 °. quadrilateral. pentagon. 3. 540 °. 4. 720 °. hexagon. 900°. heptagon. 5. octagon. 6. 1080°. 7.

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8.1 – Find Angle Measures in Polygons

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  1. 8.1 – Find Angle Measures in Polygons

  2. Angle inside a shape 2 1 2 Angle outside a shape 1 Line connecting two nonconsecutive vertices

  3. triangle 1 180°

  4. 2 360° quadrilateral

  5. pentagon 3 540°

  6. 4 720° hexagon

  7. 900° heptagon 5 octagon 6 1080° 7 1260° nonagon 8 1440° decagon n – 2 180(n – 2) n-gon

  8. The sum of the measures of the interior angles of a polygon are:_______________________ 180(n – 2) The measure of each interior angle of a regular n-gon is: 180(n – 2) n

  9. 180(n – 2) n 180(n – 2)

  10. 1. Find the sum of the measures of the interior angles of the indicated polygon. 180(n – 2) 180(7 – 2) 180(5) 900° heptagon Name __________________ Polygon Sum = __________ 900°

  11. 1. Find the sum of the measures of the interior angles of the indicated polygon. 30-gon 180(n – 2) 180(30 – 2) 180(28) 5040° 30-gon Name __________________ Polygon Sum = __________ 5040°

  12. 180(n – 2) 2. Find x. 180(5 – 2) 180(3) 540° 540° x + 90 +143 + 77 + 103 = 540 x + 413 = 540 x = 127°

  13. 2. Find x. 180(n – 2) 180(4 – 2) 180(2) 360° 360° x + 87 + 108 + 72 = 360 x + 267 = 360 x = 93°

  14. 3. Given the sum of the measures of the interior angles of a polygon, find the number of sides. 2340° 180(n – 2) = 2340 ? 180n – 360 = 2340 180n = 2700 2340° n = 15

  15. 3. Given the sum of the measures of the interior angles of a polygon, find the number of sides. 6840° 180(n – 2) = 6840 180n – 360 = 6840 180n = 7200 n = 40

  16. 4. Given the number of sides of a regular polygon, find the measure of each interior angle. 8 sides 180(n – 2) n 180(8 – 2) 8 180(6) 8 1080 8 = = = = 135° 135° ?

  17. 4. Given the number of sides of a regular polygon, find the measure of each interior angle. 18 sides 180(n – 2) n 180(18 – 2) 18 180(16) 18 2880 18 = 160° = = =

  18. 5. Given the measure of an interior angle of a regular polygon, find the number of sides. 144° 180(n – 2) n 144 = 1 144n = 180n – 360 0 = 36n – 360 360 = 36n 144° 10 = n 144°

  19. 5. Given the measure of an interior angle of a regular polygon, find the number of sides. 108° 180(n – 2) n 108 = 1 108n = 180n – 360 0 = 72n – 360 360 = 72n 5 = n

  20. Use the following picture to find the sum of the measures of the exterior angles. c ma = 70° d 120° 70° mb = 110° 50° e Sum of the exterior angles = b 130° mc = 110° 110° a 360° md = 60° me = 70°

  21. The sum of the exterior angles, one from each vertex, of a polygon is: ____________________ 360° The measure of each exterior angle of a regular n-gon is: _________________________ 360° n

  22. 360° n 360°

  23. 6. Find x. 360 x + 137 + 152 = x + 289 = 360 x = 71°

  24. 6. Find x. 360 x + 86 + 59 + 96 + 67 = x + 308 = 360 x = 52°

  25. 7. Find the measure of each exterior angle of the regular polygon. 12 sides 360° n 360° 12 30° = = ?

  26. 7. Find the measure of each exterior angle of the regular polygon. 5 sides 360° n 360° 5 72° = =

  27. 8. Find the number of sides of the regular polygon given the measure of each exterior angle. 60° 360° n 60° = 1 60n = 360 n = 6 60° 60°

  28. 8. Find the number of sides of the regular polygon given the measure of each exterior angle. 24° 360° n 24° = 1 24n = 360 n = 15

  29. MEMORIZE!!!! 180(n – 2) n 180(n – 2) 360° n 360°

  30. HW Problem #13 180(n – 2) 13. Find x. 180(8 – 2) 180(6) 1080° x+143+2x+152+116+125+140+139=1080 3x + 815 = 1080 x = 88.33°

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