Math Is Fun Forum

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?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Square & Triangle question

Hi;

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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.

mathattack

Member

Registered: 2016-03-07

Posts: 17

Re: Square & Triangle question

Thanks for the answer!  How did you get it?

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.

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°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Square & Triangle question

bobbym,

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

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

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)

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“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
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phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,880

Re: Square & Triangle question

Hi;

I also got 13°, in Geogebra.

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

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"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

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Square & Triangle question

Thanks for the diagram. 

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

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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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,880

Re: Square & Triangle question

Oo...didn't know that one!

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"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

mathattack

Member

Registered: 2016-03-07

Posts: 17

Re: Square & Triangle question

Thanks, this was great!