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

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

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

5.  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.

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

8. Exercises TELL WHETHER A POLYGON IS CONVEX OR NOT.

9. POLYGONS and its parts Review

10. POLYGON PARTS

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

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

13. ANGLE SUM MEASURES

14. Angle Sum measure of the interior angles of a polygon PolygonNo. of sidesNo. of non- overlapping diagonals No. of Triangles formed Angle Sum measure triangle3011 x 180°or 180° Quadrilateral4122 x 180°or 360° Pentagon5233 x 180°or 540° N- gonnn-3n-2(n-2)180°

15. Examples:  1. What is the sum of the measures of the interior angles of a convex polygon with  a. 11 sides  b. 15 sides Solutions: a. S a = (n – 2) 180 ⁰ = (11 – 2) 180 ⁰ = 9(180 ⁰ ) = 1620 ⁰

16. Examples:  1. What is the sum of the measures of the interior angles of a convex polygon with  a. 11 sides  b. 15 sides Solutions: b. Sa = (n – 2) 180 ⁰ = (15 – 2) 180 ⁰ = 13(180 ⁰ ) = 2340 ⁰

17. Examples:  2. Find the sum of the measures of the interior angles of a convex heptagon. Solutions: b. Sa = (n – 2) 180 ⁰ = (7 – 2) 180 ⁰ = 5(180 ⁰ ) S = 900 ⁰

18. Examples:  3. How many sides does a convex polygon have if the sum of the measures of its interior angles is 1440 ⁰ ? Solutions: b. Sa = (n – 2) 180 ⁰ 1440 ⁰ = (n – 2) 180 ⁰ 1440 = 180 ⁰ n – 360 ⁰ n = n = 10 The polygon has 10 sides.

19. 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

20. 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

21. QUIZ

22. A. FIND THE SUM OF THE MEASURES OF THE VERTEX ANGLES FOR EACH POLYGON 1. 15-gon 2. 50- gon 3. 35-gon

23. B. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN 1. 1260° 2. 1620°

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

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

27. Investigate   1,  2 and  3 are interior angles.   4,  5 and  6 are exterior angles   1 +  4 = 180°   2 +  5 = 180°   3 +  6 = 180° 11 2 3 4 5 6

28.  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 11 2 3 4 5 6

29. 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 11 2 3 4 5 6

30. 160° 70° 120° 70° 60° 110° 20° 60° 110° 60° + 60 ° + 110 ° + 20 ° + 110° = 360°

31. Angle Sum measure of the exterior angles of a polygon PolygonNo. of sides Angle Sum measure (interior angles) Measure of EACH INTERIOR angle of a regular n-gon Angle Sum measure (exterior angles) Measure of EACH exterior angle of a regular n-gon triangle31 x 180°or 180° 180° 3 360° 3 Quadrilat eral 42 x 180°or 360° 360° 4 360° 4 Pentagon53 x 180°or 540° 540° 5 360° 5 N- gonn(n-2)180° n 360° n

32. Examples:  1. How many degrees are there in each of the exterior angle of a regular hexagon? Solution: E a = E a = = 60

33. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGL E IS GIVEN 1. 30° 2. 10°

34. QUIZQUIZ

35. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN 1. 1980° 2. 4320°

36. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGLE IS GIVEN 1. 24° 2. 45°