Please help!!!!! MEDAL AND FAN!!!!!

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Please help!!!!! MEDAL AND FAN!!!!!

Mathematics
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sum of exterior angles of a polygon=360

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

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