Math Is Fun Forum

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

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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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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Polygon Angles

as shown

Got a link?

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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.

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

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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

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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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

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!

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometry Polygon Angles

hi

Yes, I make it 78 too. 

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

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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

SolarDevil

Member

Registered: 2014-09-14

Posts: 37

Re: Geometry Polygon Angles

Okay thank you so much!

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