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If ABCDE is a regular pentagon, what is the value of x in the figure

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Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
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ABCDE is a regular pentagon
Sum of all the angles of regular pentagon = (n-2) * 180 where n is the number of sides of the polygon
sum = 540
Each angle of the pentagon = 540 / 5 = 108

angle FEA = 180 - 108 =72
angle FAE = 180 - 108 = 72

Now in triangle FEA
72 + 72 + x = 180
x = 180 - 144 = 36

IMO A
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Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
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Regular pentagon: each angle = 180 x (n-2)/n = 180 x 3 / 5 = 108
FEA = FAE = 180 - 108 = 72
EFA = x = 180 - (72x2) = 180-144 = 36 (A)
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Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
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Bunuel wrote:

If ABCDE is a regular pentagon, what is the value of x in the figure above?

A. 36
B. 42
C. 45
D. 48
E. 72

Project PS Butler

Attachment:
1.png

Hi,

My analysis is as follows:

The pentagon is a closed polygon. Thus the sum of all angles is = 180 (n-2) , where n = number of vertices. In this case, n =5.
Since it is mentioned that ABCDE is a regular polygon, all angles are the same.

So, each angle = [180*(5-2)]/5 = 108 deg.
Compliment angles (interior of the triangle) = 180-108 = 72 deg.

Total sum of angles of the triangle = 180. So, x = 180 - (72*2) = 36 deg.
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Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
1
Kudos
Bunuel wrote:

If ABCDE is a regular pentagon, what is the value of x in the figure above?

A. 36
B. 42
C. 45
D. 48
E. 72

Project PS Butler

Attachment:
The attachment 1.png is no longer available

We know that sum of all external angles in a polygon is 360°.

As it is mentioned regular,All these angles are equal.

So each of the ext. angle is 72°.

So x=36'

IMO A

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Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
each angle would be 180-360/n ; 180-72 ; 108
since the ∆ is isosceles so two of its sides will be 72 each so third side would be 180-144 ; 36
option A

Bunuel wrote:

If ABCDE is a regular pentagon, what is the value of x in the figure above?

A. 36
B. 42
C. 45
D. 48
E. 72

Project PS Butler

Attachment:
1.png
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Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
1
Kudos
Bunuel wrote:

If ABCDE is a regular pentagon, what is the value of x in the figure above?

A. 36
B. 42
C. 45
D. 48
E. 72

Project PS Butler

Attachment:
1.png

Each interior angle = (n-2)/n * 180 = 108
FEA + AED = 180
FEA = 72
Similarly, FAE = 72
Now, x + 72 + 72 = 180
x = 180 - 144 = 36. IMO, (A)!
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Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
Top Contributor
Each of the internal angle in the regular pentagon ABCDE = (n-2)(pi) / 5 = 108 degrees

The external angles (Angle FEA and angle FAE) = 180 -108 = 72 degrees

Hence in the triangle AEF= 180 - (72+72)

= 180 -144 = 36 degrees (option a)

Devmitra Sen
GMAT SME
Re: If ABCDE is a regular pentagon, what is the value of x in the figure [#permalink]
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