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3.6 Angles in Polygons

3.6 Angles in Polygons. Date: _________. Sums of Interior Angles. Triangle. Quadrilateral. Pentagon. = 2 triangles. = 3 triangles. Hexagon. Octagon. Heptagon. = 4 triangles. = 5 triangles. = 6 triangles. 3. 1. 180 . 4. 360 . 2. 540 . 5. 3. 720 . 6. 4. 900 . 5. 7.

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3.6 Angles in Polygons

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  1. 3.6Angles in Polygons Date: _________

  2. Sums of Interior Angles Triangle Quadrilateral Pentagon = 2 triangles = 3 triangles Hexagon Octagon Heptagon = 4 triangles = 5 triangles = 6 triangles

  3. 3 1 180 4 360 2 540 5 3 720 6 4 900 5 7 8 6 1080 n n – 2 180•(n – 2)

  4. 135 100 70 x Find the measure of the missing angle in the figure below 135 + 100 + 70 + x = 360 305 + x = 360 -305 -305 x = 55 quadrilateral

  5. (4x + 15) 2 (5x - 5) (8x - 10) 1 3 110 Find m1. 5(20) - 5 m1 = = 95 5x - 5 + 4x + 15 + 8x - 10 + 110 + 90 = 540 17x + 200= 540 pentagon -200 -200 17x = 340 17 17 x = 20

  6. 2 1 3 5 6 4 Interior Angles Exterior Angles

  7. 2 1 3 5 6 4 Sums of Exterior Angles 180 180 180•3 = 540 180 Sum of Interior & Exterior Angles = 540 Sum of Interior Angles = 180 360 540- 180= Sum of Exterior Angles =

  8. Sums of Exterior Angles 180 180 180 180•4 = 720 180 Sum of Interior & Exterior Angles = 720 Sum of Interior Angles = 360 360 720- 360= Sum of Exterior Angles =

  9. Sum of Exterior Angles 180 180 180 180 180 180•5 = 900 900 Sum of Interior & Exterior Angles = Sum of Interior Angles = 540° 360 900- 540= Sum of Exterior Angles =

  10. Sum of Exterior Angles 180 180 180 180 180 180 180•6 = 1080 1080 Sum of Interior & Exterior Angles = Sum of Interior Angles = 720° 1080- 720= Sum of Exterior Angles = 360

  11. Sums of Exterior Angles 540 180 360 720 360 360 900 540 360 1080 720 360 Sum of Exterior Angles is always 360!

  12. Angles of Regular Polygons Sum of the Interior Angles 180(n – 2) Sum of the Exterior Angles Always 360! 180(n – 2) Each Interior Angle n Each Exterior Angle 360 n

  13. Find the sum of the measures of the interior angles of a regular dodecagon. n = 12 180•(n – 2) = 180•(12 – 2) = 180•(10) all 12 angles = 1800 What is the measure of each angle? 1800 each angle = 150 12

  14. The sum of the interior angles of a convex polygon is 1440. How many sides does the polygon have? 180•(n – 2) = 1440 180n – 360 = 1440 + 360 +360 180n = 1800 180 180 n = 10 10 sides

  15. Exterior Angles What is the measure of each exterior angle of a regular hexagon? 6 sides 360 = 60 6

  16. The measure of each exterior angle of a regular polygon is 20. How many sides does it have? 360 = 18 20 The measure of each interior angle of a regular polygon is 120. How many sides does it have? 180 - 120 60 = 360 = 6 60 exterior angle

  17. Find the sum of the interior angles of a 100-gon! Find the sum of the exterior angles of a 100-gon. Find the measure of each interior angle of a 100-gon. Find the measure of each exterior angle of a 100-gon.

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