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

- anonymous

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

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- anonymous

This is the first picture

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- anonymous

This is the second one.

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- anonymous

sum of exterior angles of a polygon=360

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## More answers

- 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

So 7-2=5*180=900

- anonymous

Is the right?

- welshfella

right

- welshfella

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

- anonymous

900-789=111

- welshfella

yes

- anonymous

So number one is 111degrees

- anonymous

How do I the rest

- anonymous

@Vocaloid

- anonymous

@freckles please help

- 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

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

- anonymous

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

- 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

but how would I find the exterior

- Michele_Laino

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

- anonymous

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

- 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

|dw:1440016841979:dw|

- anonymous

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

- Michele_Laino

yes! correct!

- anonymous

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

- Michele_Laino

ok!

- anonymous

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

- Michele_Laino

that's right!

- anonymous

How do I do number 2?

- 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

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

- Michele_Laino

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

- Michele_Laino

yes!

- Michele_Laino

oopss. 180-118, not 180-1118

- anonymous

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

- Michele_Laino

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

- anonymous

180-133=47
180-108=78

- Michele_Laino

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

- anonymous

366

- Michele_Laino

are you sure?

- anonymous

yes

- Michele_Laino

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

- anonymous

Oh ok lol. I was adding 78 not 72

- Michele_Laino

ok! :)

- anonymous

So the answer is 360?

- Michele_Laino

yes!

- 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

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

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

- Michele_Laino

we have n interior angles

- anonymous

yes

- Michele_Laino

each interior angle is 120 degrees

- Michele_Laino

I'm referring to exercise #11

- Michele_Laino

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

- Michele_Laino

n is a natural number which has to be determined

- anonymous

Ok I understand so far

- Michele_Laino

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

- Michele_Laino

for example a hexagon has 6 interior angles and 6 sides

- 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

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

- anonymous

yep

- Michele_Laino

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

- Michele_Laino

please solve for n

- anonymous

6?

- Michele_Laino

that's right!! :)

- Michele_Laino

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

- anonymous

12. 9
13. 18
14. 20

- anonymous

Is that correct?

- Michele_Laino

yes! correct!!

- anonymous

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

- Michele_Laino

thanks! :)

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