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#1 2016-03-07 15:25:37

mathattack
Member
Registered: 2016-03-07
Posts: 17

Square & Triangle question

In rectangle ABCD, we have AD = 3 and AB = 4. Let M be the midpoint of AB, and let X be the point such that MD = MX, angle MDX = 77, and A and X lie on opposite sides of DM. Find angle XCD, in degrees.

I'm trying to find out how to solve this question without using trig.  Could someone help?

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#2 2016-03-07 17:38:21

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

Re: Square & Triangle question

Hi;


In mathematics, you don't understand things. You just get used to them.
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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#3 2016-03-08 09:28:40

mathattack
Member
Registered: 2016-03-07
Posts: 17

Re: Square & Triangle question

Thanks for the answer!  How did you get it?

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#4 2016-03-08 10:21:22

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

Re: Square & Triangle question

It looks possible with Coordinate Geometry but I used Geogebra instead.


In mathematics, you don't understand things. You just get used to them.
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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#5 2016-03-08 11:39:24

harpazo
Member
Registered: 2016-03-08
Posts: 2

Re: Square & Triangle question

Angle XCD = ANGLE C.

Angle C + 77° + 90° = 180°

Angle C + 167° = 180°

Angle C = 180° - 167°

Angle C = 13°

We then say that Angle XCD = 13°.

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#6 2016-03-08 21:18:02

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

Re: Square & Triangle question

bobbym,

Please post a diagram for this.  I'm getting a very different answer. dizzy

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 2016-03-09 10:21:11

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

Re: Square & Triangle question

Hej alla!

I am getting


by two methods, no less.

Last edited by anonimnystefy (2016-03-09 10:25:37)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#8 2016-03-09 11:26:40

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,810

Re: Square & Triangle question

Hi;

I also got 13°, in Geogebra.

VNsIBMy.jpg

Last edited by phrontister (2017-02-23 11:47:06)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#9 2016-03-09 11:40:55

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

Re: Square & Triangle question

Hi Bob;

My diagram was a bit different than phrontister's but got the same answer.


In mathematics, you don't understand things. You just get used to them.
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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#10 2016-03-16 01:30:38

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

Re: Square & Triangle question

Thanks for the diagram.  smile

As MD = MX = MC, a circle centre M will go through D, X, and C.

So (by angle at edge = twice angle at the centre) DCX = half DMX.

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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#11 2016-03-16 01:45:12

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,810

Re: Square & Triangle question

Oo...didn't know that one! up


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#12 2016-03-22 08:14:31

mathattack
Member
Registered: 2016-03-07
Posts: 17

Re: Square & Triangle question

Thanks, this was great!

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