1. anonymous

This is the first picture

2. anonymous

This is the second one.

3. anonymous

sum of exterior angles of a polygon=360

4. welshfella

this is a heptagon - with 7 sides formula for number of measure of angles in an n sided polygon = 180(n -2) So plug on n = 7 and you can calculate the total measure of degrees then you can find value of x

5. anonymous

So 7-2=5*180=900

6. anonymous

Is the right?

7. welshfella

right

8. welshfella

so add up the measures of the 6 angles given and subtract form 900

9. anonymous

900-789=111

10. welshfella

yes

11. anonymous

So number one is 111degrees

12. anonymous

How do I the rest

13. anonymous

@Vocaloid

14. anonymous

15. Michele_Laino

other questions are similar, you have to use this formula: $\Large s = \left( {n - 2} \right) \times 180$ in order to compute the sum of the interior angles of a polygon

16. Michele_Laino

where n is the number of sides of your polygon, as @welshfella has written before

17. anonymous

So I type in the number of sides that the question says?

18. Michele_Laino

yes! for example, let's study exercise #5 the sum of interior angles is: $\Large s = \left( {8 - 2} \right) \times 180 = 1080$ then each interior angle measures this: $\Large \frac{{1080}}{8} = 135$

19. anonymous

but how would I find the exterior

20. Michele_Laino

the exterior angle is the supplementary angle of the corresponding interior angle: |dw:1440016538135:dw|

21. anonymous

Ok..... but how do I know how many degrees the angle is

22. Michele_Laino

for example, let's study exercise #6 since from exercise #5 we know that the measure of each interior angle is 135 degrees, then the measure of the corresponding exterior angle is: 180-135= 45 degrees

23. Michele_Laino

|dw:1440016841979:dw|

24. anonymous

3. 90 5. 135 7. 144 9. 150 Is that correct?

25. Michele_Laino

yes! correct!

26. anonymous

Ok..... I'm going to attempt to do the exterior ones

27. Michele_Laino

ok!

28. anonymous

I'm sorry if these answers are incorrect. 4. 90 6. 45 8. 36 10. 30

29. Michele_Laino

that's right!

30. anonymous

How do I do number 2?

31. Michele_Laino

you have to compute the supplementary angle of each interior angle, then you have to sum those new angles. For example: the corresponding exterior angle of the interior angle of 108 is: 180 -108 =72 the corresponding exterior angle of the angle of 133 is: 180-133= 47 and so on, please complete

32. anonymous

So I get all of the exterior angles and add them?

33. Michele_Laino

180-140=... 180-155=... 180-135=.. 180-1118=... 180-111=... since x=111

34. Michele_Laino

yes!

35. Michele_Laino

oopss. 180-118, not 180-1118

36. anonymous

180-140=40 180-155=25 180-135=45 180-118=62 180-111=69

37. Michele_Laino

ok! now what is: 40+25+62+69+47+72=...?

38. anonymous

180-133=47 180-108=78

39. Michele_Laino

yes! oops... what is 40+25+45+62+69+47+72=...? in other words you have to compute the corresponding sum

40. anonymous

366

41. Michele_Laino

are you sure?

42. anonymous

yes

43. Michele_Laino

I got this: 40+25+45+62+69+47+72=360

44. anonymous

Oh ok lol. I was adding 78 not 72

45. Michele_Laino

ok! :)

46. anonymous

47. Michele_Laino

yes!

48. anonymous

I know that I have a ton of questions and I'm sorry lol. But how do I do 11 to 14?

49. Michele_Laino

since each interior angle is 120 degrees, then the sum of all interior angles is: 120*n being n the numbers of interior angles, am I right?

50. anonymous

Idk. I'm sorry. I'm a bit confused

51. Michele_Laino

we have n interior angles

52. anonymous

yes

53. Michele_Laino

each interior angle is 120 degrees

54. Michele_Laino

I'm referring to exercise #11

55. Michele_Laino

so the sum of all interior angles is: 120*n

56. Michele_Laino

n is a natural number which has to be determined

57. anonymous

Ok I understand so far

58. Michele_Laino

now, since our polygon has n interior angles, then it also has n sides

59. Michele_Laino

for example a hexagon has 6 interior angles and 6 sides

60. Michele_Laino

now I use the general formula for the sum of interior angles: $\Large s = \left( {n - 2} \right) \times 180$ and I can write this: $\Large \left( {n - 2} \right) \times 180 = 120 \times n$

61. Michele_Laino

since, as we noted before, s=120*n

62. anonymous

yep

63. Michele_Laino

now I simplify the left side, so i get: $\Large 180 \times n - 360 = 120 \times n$

64. Michele_Laino

65. anonymous

6?

66. Michele_Laino

that's right!! :)

67. Michele_Laino

exercises #12, #13, and #14 are similar

68. anonymous

12. 9 13. 18 14. 20

69. anonymous

Is that correct?

70. Michele_Laino

yes! correct!!

71. anonymous

Thank a bunch!!! I thought I'd never understand those problems lol.

72. Michele_Laino

thanks! :)