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EXERCISES

EXERCISES. TELL WHETHER OR NOT EACH OF THE FOLLOWING IS A POLYGON. Exercises. TELL WHETHER A POLYGON IS CONVEX OR NOT. POLYGONS and its parts. Review. POLYGON PARTS. POLYGON PARTS. Vertex - point where two sides meet. Two or more of these points are called vertices.

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EXERCISES

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

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

  3. POLYGONS and its parts Review

  4. POLYGON PARTS

  5. 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.

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

  7. ANGLE SUM MEASURES

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

  9. 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

  10. 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

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. QUIZ

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

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

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

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

  20. 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

  21. 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

  22. 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

  23. 20° 160° 110° 70° 70° 110° 60° 120° 120° 60° 60° + 60 ° + 110 ° + 20 ° + 110° = 360°

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

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

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

  27. QUIZ

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

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

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