anonymous
  • anonymous
Please help!!!!! MEDAL AND FAN!!!!!
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
This is the first picture
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anonymous
  • anonymous
This is the second one.
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anonymous
  • anonymous
sum of exterior angles of a polygon=360

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welshfella
  • 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
anonymous
  • anonymous
So 7-2=5*180=900
anonymous
  • anonymous
Is the right?
welshfella
  • welshfella
right
welshfella
  • welshfella
so add up the measures of the 6 angles given and subtract form 900
anonymous
  • anonymous
900-789=111
welshfella
  • welshfella
yes
anonymous
  • anonymous
So number one is 111degrees
anonymous
  • anonymous
How do I the rest
anonymous
  • anonymous
@Vocaloid
anonymous
  • anonymous
@freckles please help
Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
where n is the number of sides of your polygon, as @welshfella has written before
anonymous
  • anonymous
So I type in the number of sides that the question says?
Michele_Laino
  • 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: \[\Large \frac{{1080}}{8} = 135\]
anonymous
  • anonymous
but how would I find the exterior
Michele_Laino
  • Michele_Laino
the exterior angle is the supplementary angle of the corresponding interior angle: |dw:1440016538135:dw|
anonymous
  • anonymous
Ok..... but how do I know how many degrees the angle is
Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
|dw:1440016841979:dw|
anonymous
  • anonymous
3. 90 5. 135 7. 144 9. 150 Is that correct?
Michele_Laino
  • Michele_Laino
yes! correct!
anonymous
  • anonymous
Ok..... I'm going to attempt to do the exterior ones
Michele_Laino
  • Michele_Laino
ok!
anonymous
  • anonymous
I'm sorry if these answers are incorrect. 4. 90 6. 45 8. 36 10. 30
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
How do I do number 2?
Michele_Laino
  • 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
anonymous
  • anonymous
So I get all of the exterior angles and add them?
Michele_Laino
  • Michele_Laino
180-140=... 180-155=... 180-135=.. 180-1118=... 180-111=... since x=111
Michele_Laino
  • Michele_Laino
yes!
Michele_Laino
  • Michele_Laino
oopss. 180-118, not 180-1118
anonymous
  • anonymous
180-140=40 180-155=25 180-135=45 180-118=62 180-111=69
Michele_Laino
  • Michele_Laino
ok! now what is: 40+25+62+69+47+72=...?
anonymous
  • anonymous
180-133=47 180-108=78
Michele_Laino
  • Michele_Laino
yes! oops... what is 40+25+45+62+69+47+72=...? in other words you have to compute the corresponding sum
anonymous
  • anonymous
366
Michele_Laino
  • Michele_Laino
are you sure?
anonymous
  • anonymous
yes
Michele_Laino
  • Michele_Laino
I got this: 40+25+45+62+69+47+72=360
anonymous
  • anonymous
Oh ok lol. I was adding 78 not 72
Michele_Laino
  • Michele_Laino
ok! :)
anonymous
  • anonymous
So the answer is 360?
Michele_Laino
  • Michele_Laino
yes!
anonymous
  • anonymous
I know that I have a ton of questions and I'm sorry lol. But how do I do 11 to 14?
Michele_Laino
  • 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?
anonymous
  • anonymous
Idk. I'm sorry. I'm a bit confused
Michele_Laino
  • Michele_Laino
we have n interior angles
anonymous
  • anonymous
yes
Michele_Laino
  • Michele_Laino
each interior angle is 120 degrees
Michele_Laino
  • Michele_Laino
I'm referring to exercise #11
Michele_Laino
  • Michele_Laino
so the sum of all interior angles is: 120*n
Michele_Laino
  • Michele_Laino
n is a natural number which has to be determined
anonymous
  • anonymous
Ok I understand so far
Michele_Laino
  • Michele_Laino
now, since our polygon has n interior angles, then it also has n sides
Michele_Laino
  • Michele_Laino
for example a hexagon has 6 interior angles and 6 sides
Michele_Laino
  • 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: \[\Large \left( {n - 2} \right) \times 180 = 120 \times n\]
Michele_Laino
  • Michele_Laino
since, as we noted before, s=120*n
anonymous
  • anonymous
yep
Michele_Laino
  • Michele_Laino
now I simplify the left side, so i get: \[\Large 180 \times n - 360 = 120 \times n\]
Michele_Laino
  • Michele_Laino
please solve for n
anonymous
  • anonymous
6?
Michele_Laino
  • Michele_Laino
that's right!! :)
Michele_Laino
  • Michele_Laino
exercises #12, #13, and #14 are similar
anonymous
  • anonymous
12. 9 13. 18 14. 20
anonymous
  • anonymous
Is that correct?
Michele_Laino
  • Michele_Laino
yes! correct!!
anonymous
  • anonymous
Thank a bunch!!! I thought I'd never understand those problems lol.
Michele_Laino
  • Michele_Laino
thanks! :)

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