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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 The sum of the measures of the interior angles of a polygon are:_______________________ 180(n – 2)

  8. The measure of each interior angle of a regular n-gon is: 180(n – 2) n

  9. Find the sum of the measures of the interior angles of the indicated polygon. 18-gon 180(n – 2) 180(18 – 2) 180(16) 2880°

  10. 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°

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

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

  13. 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 n = 15

  14. 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

  15. 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°

  16. 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°

  17. Given the measure of each 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 10 = n

  18. Given the measure of each 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

  19. Use the following picture to find the sum of the measures of the exterior angles. ma = 110° mb = 60° Sum of the exterior angles = mc = 100° 360° md = 90°

  20. The sum of the exterior angles, one from each vertex, of a polygon is: ____________________ 360°

  21. The measure of each exterior angle of a regular n-gon is: _________________________ 360° n

  22. Find x. 360 x + 137 + 152 = x + 289 = 360 x = 71°

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

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

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

  26. 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

  27. 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

  28. 180(n – 2) n 180(n – 2) 360° n 360°

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

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