Please solve: regular pentagon ABCDE; FE, EG, GH sides of regular n-gon; AB horizontal, EG vertical; m(<DEF)=69degrees

I subtract 69 from 72 which is an exterior angle of a regular polygon. That answer 3° (72-69) is in the require polygon so I can't count that as an exterior angle. I can't figure out how to calculate the value of n.
 
Laia said:
I subtract 69 from 72 which is an exterior angle of a regular polygon. That answer 3° (72-69) is in the require polygon so I can't count that as an exterior angle. I can't figure out how to calculate the value of n.
Click to expand...
By extending the lines EG & AB as shown below...
(I have helpfully added the interior angle of the pentagon 🙂)

You should now be able to (easily, I trust 😉) calculate in turn the sizes of the angles 1, 2, 3, 4 and 5 (which is the exterior angle of the n-polygon).

Once you have the exterior angle of the n-polygon you should be able to calculate its interior angle and, thence, the value of n.

If you are at all unsure how to proceed from there then read these pages first:-

Hope that helps. 😊

Polygon.png​
 
The Highlander said:
By extending the lines EG & AB as shown below...
(I have helpfully added the interior angle of the pentagon 🙂)

You should now be able to (easily, I trust 😉) calculate in turn the sizes of the angles 1, 2, 3, 4 and 5 (which is the exterior angle of the n-polygon).

Once you have the exterior angle of the n-polygon you should be able to calculate its interior angle and, thence, the value of n.

If you are at all unsure how to proceed from there then read these pages first:-

Hope that helps. 😊

Click to expand...
Thank you! I'll try to find the answer by using the mentioned method.
 
The Highlander said:
By extending the lines EG & AB as shown below...
(I have helpfully added the interior angle of the pentagon 🙂)

You should now be able to (easily, I trust 😉) calculate in turn the sizes of the angles 1, 2, 3, 4 and 5 (which is the exterior angle of the n-polygon).

Once you have the exterior angle of the n-polygon you should be able to calculate its interior angle and, thence, the value of n.

If you are at all unsure how to proceed from there then read these pages first:-

Hope that helps. 😊

Click to expand...
The exterior angle (angle 5 in the photo) is 15° and the value of n is 24. Is that correct? Since the Pentagon is a regular polygon, all of it's interior angles are 108. So the angle 2 in the picture is 72° and the angle happened by connecting the line from AB and EG is 90. So The value of angle 3 is 18. And then I used the angle on straight line is 180° theorem to find the angle 4 and 5.
 
Laia said:
The exterior angle (angle 5 in the photo) is 15° and the value of n is 24. Is that correct? Since the Pentagon is a regular polygon, all of it's interior angles are 108. So the angle 2 in the picture is 72° and the angle happened by connecting the line from AB and EG is 90. So The value of angle 3 is 18. And then I used the angle on straight line is 180° theorem to find the angle 4 and 5.
Click to expand...
Yes, @Laia, n is 24 but where is your sketch?

And, more importantly, where is your working?

How did you arrive at n = 24?

You have explained, in words, how you got the exterior angle to be 15° which was fine but that was the easy part!

I laid out a path for you to "walk through" the angles in turn to get the exterior angle as 15° but you haven't shown us how you got from that to the interior angle of the n-polygon or, once you knew that, how you determined a value for n.

Where is your working? (A picture of what you scribbled on a scrap of paper would be sufficient. 😊)

It would just be nice if you were to show us some of the work you have done in return for the work we have done to help you towards a solution of your problem, no?
 
I didn't calculate the value of interior angle since the question doesn't ask for it and only ask the value of n which can be angles or sides yet in the question the n is for sides and thus I only searched for the value of sides.
 

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The Highlander said:
Yes, @Laia, n is 24 but where is your sketch?

And, more importantly, where is your working?

How did you arrive at n = 24?

You have explained, in words, how you got the exterior angle to be 15° which was fine but that was the easy part!

I laid out a path for you to "walk through" the angles in turn to get the exterior angle as 15° but you haven't shown us how you got from that to the interior angle of the n-polygon or, once you knew that, how you determined a value for n.

Where is your working? (A picture of what you scribbled on a scrap of paper would be sufficient. 😊)

It would just be nice if you were to show us some of the work you have done in return for the work we have done to help you towards a solution of your problem, no?
Click to expand...
I apologise for not showing my sketch. Also, thanks a ton for helping on this!!!
 
Laia said:
I apologise for not showing my sketch. Also, thanks a ton for helping on this!!!
Click to expand...
Thank you for showing us your sketch, @Amelinator, and very nice it is too! Well done! :thumbup:

But the question clearly said: "Calculate the value of n".

Did you just find some website or other that told you that, if a polygon's exterior angle was 15°, then it had 24 sides?

That was very clever (and efficient 😉) of you but was a bit of a cheat wasn't it? 🤣

I gave you a link to a website that told you the formula linking interior angles and the number of sides for any polygon. Did you not read through that?

I would have thought that the aim of this exercise was to ensure that you knew this stuff and could do the calculation(s); not just prove you're a good web surfer. 😄

It might be a good idea for you to go and read the websites I directed you to and then have a shot at doing the actual calculation to get the value of n.

I can't force you, clearly, but let us know whether you'll be willing to try, eh?
 
First of all,please do not accuse me of those AI related solving stuffs. My school math teacher taught the formula to calculate the one exterior angle of a polygon. Which exterior angle = 360/n. And I use that formula.I already know the formulas too. This is kind of mean for you to accuse me like this😅 Besides this, I'm still thankful for your helps.
 
The Highlander said:
Thank you for showing us your sketch, @Amelinator, and very nice it is too! Well done! :thumbup:

But the question clearly said: "Calculate the value of n".

Did you just find some website or other that told you that, if a polygon's exterior angle was 15°, then it had 24 sides?

That was very clever (and efficient 😉) of you but was a bit of a cheat wasn't it? 🤣

I gave you a link to a website that told you the formula linking interior angles and the number of sides for any polygon. Did you not read through that?

I would have thought that the aim of this exercise was to ensure that you knew this stuff and could do the calculation(s); not just prove you're a good web surfer. 😄

It might be a good idea for you to go and read the websites I directed you to and then have a shot at doing the actual calculation to get the value of n.

I can't force you, clearly, but let us know whether you'll be willing to try, eh?
Click to expand...
I did calculate the value of n using the formula tho. Why did you accuse me like that 🥲 I clearly show the calculation too.
 
Laia said:
First of all,please do not accuse me of those AI related solving stuffs. My school math teacher taught the formula to calculate the one exterior angle of a polygon. Which exterior angle = 360/n. And I use that formula.I already know the formulas too. This is kind of mean for you to accuse me like this😅 Besides this, I'm still thankful for your helps.
Click to expand...
Sorry. Didn't mean to upset you. 🫢🙏🤷‍♂️
I had just hoped to see you using the interior angle formula: \(\displaystyle \frac{(n-2)\times 180°}{n}\)
I was looking forward to seeing your Algebra skills at work (and didn't read all the way down your working).
My bad. 😔
 
The Highlander said:
Sorry. Didn't mean to upset you. 🫢🙏🤷‍♂️
I had just hoped to see you using the interior angle formula: \(\displaystyle \frac{(n-2)\times 180°}{n}\)
I was looking forward to seeing your Algebra skills at work (and didn't read all the way down your working).
My bad. 😔
Click to expand...
Well I had a thought to use it but instead I used the way which is less time-consuming.
 
Laia said:
Well I had a thought to use it but instead I used the way which is less time-consuming.
Click to expand...
And quicker too! 😉

That's why, when I looked at your picture and didn't see several lines of algebra included (I was too impressed by your very neat & accurate drawing of the figure! 😲), I immediately jumped to the (erroneous) conclusion that you'd got the value for n without any calculation.

Given that the interior angle is 180° - n ie: 165°, can you use that formula to calculate n?

Go on, I dare you! 🤣
 
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