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Finding the Sum of the Interior Angles and Exterior Angles of Any Polygon.

Finding the Sum of the Interior Angles and Exterior Angles of Any Polygon. What have you learned?. Answer each question as indicated. What is the sum measures of the interior angles of a triangle? Answer: 180 . What have you learned?. Answer each question as indicated.

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Finding the Sum of the Interior Angles and Exterior Angles of Any Polygon.

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  1. Finding the Sum of the Interior Angles and Exterior Angles of Any Polygon.

  2. What have you learned? Answer each question as indicated. What is the sum measures of the interior angles of a triangle? Answer: 180

  3. What have you learned? Answer each question as indicated. What is the measure of each angle of an equilateral triangle? Answer: 60

  4. What have you learned? Answer each question as indicated. What is the sum measures of the interior angles of a quadrilateral? Answer: 360

  5. What you are expected to learn • Determine the sum of the measures of the interior and exterior angles of the triangle. • Determine the sum of the measures of the interior and exterior angles of a quadrilateral. • Make generalizations on the sum of the measures of the interior and exterior angles of a polygon.

  6. EXERCISES • TELL WHETHER OR NOT EACH OF THE FOLLOWING IS A POLYGON.

  7. Exercises • TELL WHETHER A POLYGON IS CONVEX OR NOT.

  8. POLYGONS and its parts Review

  9. POLYGON PARTS

  10. POLYGON PARTS Vertex - point where two sides meet. Two or more of these points are called vertices. Side - one of the line segments that make up the polygon.

  11. POLYGON PARTS Diagonal - a line connecting two vertices that isn't a side.

  12. ANGLE SUM MEASURES

  13. Angle Sum measure of the interior angles of a polygon

  14. Examples: Solutions: a. Sa = (n – 2) 180⁰ = (11 – 2) 180⁰ = 9(180⁰) = 1620⁰ • 1. What is the sum of the measures of the interior angles of a convex polygon with • a. 11 sides • b. 15 sides

  15. Examples: Solutions: b. Sa = (n – 2) 180 ⁰ = (15 – 2) 180⁰ = 13(180⁰) = 2340⁰ • 1. What is the sum of the measures of the interior angles of a convex polygon with • a. 11 sides • b. 15 sides

  16. Examples: Solutions: b. Sa = (n – 2) 180⁰ = (7 – 2) 180 ⁰ = 5(180 ⁰) S = 900⁰ • 2. Find the sum of the measures of the interior angles of a convex heptagon.

  17. Examples: Solutions: b. Sa = (n – 2) 180⁰ 1440⁰ = (n – 2) 180⁰ 1440 = 180⁰ n – 360⁰ n = n = n = 10 • 3. How many sides does a convex polygon have if the sum of the measures of its interior angles is 1440⁰? The polygon has 10 sides.

  18. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN 4. 1260° S=(n-2)180 1260 =180n-360 1260+360= 180n 1620 = 180n n= 9

  19. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN 4. 1260° n =(S180) + 2 = (1260  180) + 2 = 7 + 2 n= 9

  20. QUIZ

  21. A. FIND THE SUM OF THE MEASURES OF THE VERTEX ANGLES FOR EACH POLYGON 15-gon 50- gon 35-gon

  22. B. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN 1260° 1620°

  23. Angle Sum Measures of the Exterior Angles of a Polygon LESSON 7

  24. POLYGON PARTS Exterior Angle - Angle formed by two adjacent sides outside the polygon. Interior Angle - Angle formed by two adjacent sides inside the polygon.

  25. Investigate • 1, 2 and 3 are interior angles. • 4,5 and 6 are exterior angles • 1 + 4 = 180° • 2 + 5 = 180° • 3 + 6 = 180° 6 3 1 1 2 5 4

  26. If m1= 70, what is the measure 4? • m4= 110 • If m2 = 80, what is the m5? • m5= 100 • If m3 = 30, what is the m6? • m6= 150 6 3 1 1 2 5 4

  27. The sum of the exterior angles of an n-gon is 360° • m4= 110 • m5= 100 • m6= 150 • m2 + m4 + m6=360 6 3 1 1 2 5 4

  28. 20° 160° 110° 70° 70° 110° 60° 120° 120° 60° 60° + 60 ° + 110 ° + 20 ° + 110° = 360°

  29. Angle Sum measure of the exterior angles of a polygon

  30. Examples: Solution: Ea = Ea = = 60 • 1. How many degrees are there in each of the exterior angle of a regular hexagon?

  31. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGL E IS GIVEN 30° 10°

  32. QUIZ

  33. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN 1980° 4320°

  34. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGLE IS GIVEN 24° 45°

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