In the figure below, AB=BC=CD=DE=EF=FG=GA. Then angle DAE is approximately?
a. 15
b. 20
c. 30
d. 25
e. 45
[/img]
geometry question
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- hemant_rajput
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[/img]hemant_rajput wrote:In the figure below, AB=BC=CD=DE=EF=FG=GA. Then angle DAE is approximately?
Let us assume, DAE = x
Triangle ABC is isosceles as AB = BC --> BCA = CAB = x
Hence, CBD = CAB + BCA = x + x = 2x .............. [External angle of triangle ABC]
Triangle BCD is isosceles as BC = CD --> CBD = CDB = 2x
Hence, DCE = DAE + CDA = x + 2x = 3x .............. [External angle of triangle ACD]
Triangle CDE is isosceles as CD = DE --> DCE = DEC = AED = 3x
Similarly, ADE = EFD = AEF + DAE = EGF + DAE = (DAE + GFA) + DAE = DAE + DAE + DAE = 3x
Hence, in triangle ADE, ADE + DAE + AED = 3x + x + 3x = 7x
Hence, 7x = 180 ---> x = 180/7 = 25.7.. ≈ 25
The correct answer is D.
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- hemant_rajput
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How come GFA = DAE?Anurag@Gurome wrote:[/img]hemant_rajput wrote:In the figure below, AB=BC=CD=DE=EF=FG=GA. Then angle DAE is approximately?
Let us assume, DAE = x
Triangle ABC is isosceles as AB = BC --> BCA = CAB = x
Hence, CBD = CAB + BCA = x + x = 2x .............. [External angle of triangle ABC]
Triangle BCD is isosceles as BC = CD --> CBD = CDB = 2x
Hence, DCE = DAE + CDA = x + 2x = 3x .............. [External angle of triangle ACD]
Triangle CDE is isosceles as CD = DE --> DCE = DEC = AED = 3x
Similarly, ADE = EFD = AEF + DAE = EGF + DAE = (DAE + GFA) + DAE = DAE + DAE + DAE = 3x
Hence, in triangle ADE, ADE + DAE + AED = 3x + x + 3x = 7x
Hence, 7x = 180 ---> x = 180/7 = 25.7.. ≈ 25
The correct answer is D.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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In triangle GAF, FG = GA ---> GAF = GFAhemant_rajput wrote:How come GFA = DAE?
Now, GAF is nothing but DAE.
Hence, GFA = DAE
Hope that helps.
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I'm going to say "no"mariofelixpasku wrote:can we expect such a question on the gmat ?
More than anything, it's too time-consuming. Simply drawing the diagram on scratch paper and labeling all of the equivalent lines (AB=BC=CD=DE=EF=FG=GA) will eat up a ton of time, and that's BEFORE any actual calculations begin.
IMPORTANT: On a Problem Solving question involving geometric figures, the diagram will be drawn to scale, unless it's stated otherwise. So, even if we don't know how to solve the question, we can probably eliminate one or two answer choices. In this case, the angle looks bigger than 15 degrees and less than 45 degrees. So, then we'd guess B, C or D.
Cheers,
Brent
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