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Angles of Polygons

Angles of Polygons. Notes 21 – Section 6.1. Essential Learnings. Students will understand and be able to determine the sum of the interior and exterior angles of polygons. Students will be able to solve problems involving polygons. Vocabulary.

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Angles of Polygons

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  1. Angles of Polygons Notes 21 – Section 6.1

  2. Essential Learnings • Students will understand and be able to determine the sum of the interior and exterior angles of polygons. • Students will be able to solve problems involving polygons.

  3. Vocabulary • Diagonal – a segment that connects any two nonconsecutive vertices.

  4. Sum of Interior Angle Measures

  5. Polygon Interior Angles Sum • The sum of the interior angle measures of an n-sided convex polygon is (n – 2) • 180. mA + mB + mC + mD + mE = (5 – 2)  180 = 540 B A C E D

  6. Example 1 • Find the sum of the measures of the interior angles of each convex polygon. Decagon 18-gon

  7. Example 2 • Find the sum of the measure of each interior angle. (5x)⁰ (11x+4)⁰ (11x+4)⁰ (5x)⁰

  8. Example 3 • Find the sum of the measures of the interior angles of each regular polygon. hexagon decagon

  9. Example 4 • The measure of an interior angle of a regular polygon is 150. Find the number of sides in the polygon.

  10. Polygon Exterior Angles Sum • The sum of the exterior angle measures of a convex polygon, one angle at each vertex, is 360⁰. m1 + m2 + m3 + m4 + m5 = 360. 2 1 3 5 4

  11. Example 5 • Find the value of x in the diagram. 5x 5x + 5 4x - 6 2x + 3 5x - 5 4x + 3 6x - 12

  12. Example 6 • Find the measure of each exterior angle of a regular dodecagon.

  13. Assignment Pages 395: 12-19, 21-24, 26-37, 45 Math’s Mates 2-4 Due Friday! Mastery Assignment

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