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If ABCD is square and both AED and CDF are equilateral triangles, what

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MathRevolution
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If ABCD is square and both AED and CDF are equilateral triangles, what [#permalink] New post   12 Mar 2016, 06:37
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A
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C
D
E

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45% (medium)

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ABCD.jpg [ 5.87 KiB | Viewed 5825 times ]

If ABCD is square and both AED and CDF are equilateral triangles, what is the angle FGC?

A. 45o
B. 50o
C. 60o
D. 75o
E. 80o


* A solution will be posted in two days.
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C
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chetan2u
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If ABCD is square and both AED and CDF are equilateral triangles, what [#permalink] New post   12 Mar 2016, 09:53
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MathRevolution wrote:
Attachment:
The attachment ABCD.jpg is no longer available

If ABCD is square and both AED and CDF are equilateral triangles, what is the angle FGC?

A. 45o
B. 50o
C. 60o
D. 75o
E. 80o


* A solution will be posted in two days.


Hi,

since it seems to be a complicated pics, let me label and draw again. pl see att figure


let each side of square be x, so each side of equilateral side will also be x..

1) lets see the triangle ADF
angle D= 90+60=150
AD=DF=x so isosceles triangle..
angle DAF and Angle DFA= (180-150)/2=15

2) similarily in triangle CDE
angle DEC= angle DCE=15..

3) lets see the polygon in center which has D and G as opposite vertices...
angle D=90..
angle on the other two vertices= 180-90-15=75..
so all angles in this polygon=90+75+75+G=240+G=360..
so G= 120.

we are looking for angle ?...
G + ?=180..
120+?=180
?=60
ans C
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Re: If ABCD is square and both AED and CDF are equilateral triangles, what [#permalink] New post   14 Mar 2016, 18:04
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If ABCD is square and both AED and CDF are equilateral triangles, what is the angle FGC?

A. 45o
B. 50o
C. 60o
D. 75o
E. 80o


-> Angle ADC=90 degrees, angle DEC=angle DCE=angle DFA=angle DAF=15 degrees. Then, angle DCF=60 degrees and angle GFC=45 degrees, which makes angle G=60 degrees. Therefore, the answer is C.
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If ABCD is square and both AED and CDF are equilateral triangles, what [#permalink] New post   22 Oct 2016, 22:12
MathRevolution wrote:
Attachment:
ABCD.jpg

If ABCD is square and both AED and CDF are equilateral triangles, what is the angle FGC?

A. 45o
B. 50o
C. 60o
D. 75o
E. 80o


* A solution will be posted in two days.

Not sure if my approach is right .But here is what I thought.

Given ABCD is a square , AD,DC,AE,ED,DF,FC all are equal.
So EC and AF should be equal as angles ADE and CDF are both 60 each.
In the original AED construct all are 60 each.
angle AED = angle AEG + angle GED
or loss of angle GED is gained by angle GAD in the triangle .
as everything got balanced , angle EDA should be angle EGA or angle FGC => 60
Answer is C
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Re: If ABCD is square and both AED and CDF are equilateral triangles, what [#permalink] New post   04 May 2023, 03:55
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Re: If ABCD is square and both AED and CDF are equilateral triangles, what [#permalink]
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