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Objectives: Develop and use formulas for the sums of the

3.6 Angles in Polygons. Objectives: Develop and use formulas for the sums of the measures of interior and exterior angles of polygons. Warm-Up:.

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Objectives: Develop and use formulas for the sums of the

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  1. 3.6 Angles in Polygons Objectives: Develop and use formulas for the sums of the measures of interior and exterior angles of polygons Warm-Up: Here’s a two part puzzle designed to prove that half of eleven is six. First rearrange two sticks to reveal the number eleven. Then remove half of the sticks to reveal the number six.

  2. Convex Polygon: A polygon in which any line segment connecting two points of the polygon has no part outside the polygon.

  3. Concave Polygon: A polygon that is not convex.

  4. Consider the following Pentagon: Divide the polygon into three triangular regions by drawing all the possible diagonals from one vertex. Add the three expressions: Find each of the following:

  5. Note: You can form triangular regions by drawing all possible diagonals from a given vertex of any polygon # of triangular regions Sum of Interior angles # of sides Polygon Triangle 3 1 180 2 360 4 Quadrilateral 540 5 Pentagon 3 4 720 6 Hexagon n n2 n-gon 180(n-2)

  6. The sum of the measures of the interior angles of a polygon with n sides is: 180(n-2)

  7. Note: Recall that a regular polygon is on in which all the angles are congruent. Sum of Interior angles Measure of Interior angles # of sides Polygon Triangle 3 180 60 360 90 4 Quadrilateral 540 5 Pentagon 108 120 720 6 Hexagon 180(n-2) n n n-gon 180(n-2)

  8. The measure of an Interior Angle of a Regular Polygon with n sides is: 180(n-2) n

  9. Exterior Angle Sums in Polygons

  10. Sum of Exterior angles Sum of interior & exterior angles Sum of Interior angles # of sides Polygon Triangle 3 180 540 360 360 720 4 Quadrilateral 360 900 540 5 Pentagon 360 1080 720 360 6 Hexagon n 180n 360 n-gon 180(n-2)

  11. Theorem Sum of the measures of the Exterior Angles of a Polygon is:

  12. Find the indicated angle measures.

  13. Find the indicated angle measures.

  14. Find the indicated angle measures.

  15. Find the indicated angle measures.

  16. For each polygon determine the measure of an interior angle and the measure of an exterior angle. A rectangle An equilateral triangle A regular dodecagon An equiangular pentagon

  17. An interior angle measure of a regular polygon is given. Find the number of sides of the polygon

  18. An exterior angle measure of a regular polygon is given. Find the number of sides of the polygon

  19. Find the indicated angle measure.

  20. Find the indicated angle measure.

  21. Find the indicated angle measure.

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