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Angles of Polygons

Angles of Polygons. Find the sum of the measures of the interior angles of a polygon Find the sum of the measures of the exterior angles of a polygon. This scallop resembles a 12-sided polygon with diagonals drawn from one of the vertices. SUM OF MEASURES OF INTERIOR ANGLES.

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Angles of Polygons

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  1. Angles of Polygons • Find the sum of the measures of the interior angles of a • polygon • Find the sum of the measures of the exterior angles of a • polygon This scallop resembles a 12-sided polygon with diagonals drawn from one of the vertices.

  2. SUM OF MEASURES OF INTERIOR ANGLES Polygons with more than 3 sides have diagonals. Quadrilateral

  3. SUM OF MEASURES OF INTERIOR ANGLES Polygons with more than 3 sides have diagonals. Pentagon

  4. SUM OF MEASURES OF INTERIOR ANGLES Polygons with more than 3 sides have diagonals. Hexagon

  5. SUM OF MEASURES OF INTERIOR ANGLES Polygons with more than 3 sides have diagonals. Heptagon

  6. SUM OF MEASURES OF INTERIOR ANGLES Polygons with more than 3 sides have diagonals. Octagon

  7. Theorem 8.1 Interior Angle Sum Theorem If a convex polygon has n sides then the sum Sof the measures of its interior angles is: S = 180(n - 2)

  8. EXAMPLE 1 Find the sum of the interior angles of the pentagon. N = 5 S = 180(n – 2) = 180(5 – 2) or 540

  9. Convex Polygons What is the exterior angle of each regular polygon? Is thetotal360°in each case?

  10. Interior Angles of Polygons Find the unknown angles below. x 100° w 90° 75° 120° 120° 75° 70° (5 – 2) x 180° = 540° 540 – = (4 – 2) x 180° = 360° 360 – 245 = 115° 125o 130o 136o z 125o 100o 112o 136o 108o y 134o 122o 126o (6 – 2) x 180° = 720° 720 – = (7 – 2) x 180° =

  11. Interior Angles of Polygons Calculate the angle sum and interior angle of each of these regular polygons. 2 3 4 1 9 sides 7 sides 10 sides 11 sides Nonagon Septagon/Heptagon Decagon Hendecagon 900°/128.6° 6 7 5 12 sides 16 sides 20 sides Hexadecagon Icosagon Dodecagon

  12. EXAMPLE 2 Find the measure of each interior angle n = 4 B C 2x° 2x° Sum of interior angles is 180(4 – 2) or 360 x° x° A D

  13. Exterior Angles of Polygons Exterior Angle Theorem The exterior angle of a triangle is equal to the sum of the remote interior angles. remote interior angles A exterior angle B C D i.e. ACD = ABC + BAC

  14. Theorem 8.1 Exterior Angle Sum Theorem If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° 2 1 3 5 4

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