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#1 2014-09-14 12:52:18

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

Geometry Polygon Angles

Hey! I have had some trouble figuring out this problem and would like some help, please show me your solution!

A regular heptagon and a regular 15-gon share a common edge AB, as shown. Find angle BCD, in degrees.

Sorry I didn't supply a drawing.

Thanks
SolarDevil


Herro! Sycamore School will win National Science Bowl this year!!! big_smile

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#2 2014-09-14 13:08:19

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Geometry Polygon Angles

Well, it's hard to solve, considering we have no idea where C and D are.


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#3 2014-09-14 14:02:16

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Geometry Polygon Angles

as shown

Got a link?


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If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#4 2014-09-14 19:36:04

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Geometry Polygon Angles

hi SolarDevil

Welcome to the forum.

It's tricky without knowing which points are C and D.  I've labelled the centres as C and D but I doubt that's the points you mean.

dREs4Rh.gif

You can work out ACB with 360/15, and as it's an isosceles triangle, you can then get CAB.

Similarly, ADB = 360/7 and then get DAB.

If that's not enough to get the angle you want, you'll have to post back, describing which points you mean in words.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2014-09-15 00:30:36

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

Re: Geometry Polygon Angles

Sorry for the late reply. Points C and D are on the heptagon and the 15-gon respectively where C and D are adjacent to point A.

Thanks
SolarDevil


Herro! Sycamore School will win National Science Bowl this year!!! big_smile

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#6 2014-09-15 01:43:32

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Geometry Polygon Angles

hi SolarDevil

OK.  That makes sense.

With A as centre a circle radius AB will also go through C and D.

Work out the internal angles for each (180 - 360/n) and hence CAD.

This triangle (CAD) is isosceles so you can calculate ACD.

Also ABC is isosceles so you can calculate ACB.

Together these will give you BCD.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#7 2014-09-15 10:17:40

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

Re: Geometry Polygon Angles

Thank you so much! So the answer would be 78? If not, what are my errors.
Once again, thank you so much!


Herro! Sycamore School will win National Science Bowl this year!!! big_smile

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#8 2014-09-15 19:46:28

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Geometry Polygon Angles

hi

Yes, I make it 78 too.  smile

Sorry, I slipped up with my internal angle formula.  Good to see it didn't stop you getting it right.  I've edited it now.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#9 2014-09-17 11:47:47

SolarDevil
Member
Registered: 2014-09-14
Posts: 37

Re: Geometry Polygon Angles

Okay thank you so much!


Herro! Sycamore School will win National Science Bowl this year!!! big_smile

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