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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If ABCDE is a regular pentagon, what is the value of x in the figure a  [#permalink]

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16 Oct 2016, 05:43
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Difficulty:

15% (low)

Question Stats:

79% (01:28) correct 21% (02:06) wrong based on 73 sessions

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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

Attachment:

T6103.png [ 7.89 KiB | Viewed 3210 times ]

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Concentration: Operations, Entrepreneurship
Re: If ABCDE is a regular pentagon, what is the value of x in the figure a  [#permalink]

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16 Oct 2016, 06:52
Sum of angles of pentagon = (5-2)*180 = 540

Individual angle of regular pentagon = 540/5 = 108

The sum of angles of quadrilateral BCDF = 360

108+108+108+x=360

x=36

A

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

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16 Oct 2016, 08:30
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

Attachment:
T6103.png

Exterior angle = 360/n where n is the number of sides of polygon

So the exterior angles at points A and E = 360/5 = 72

Now, Sum of the angles in Triangle AFE = x+72+72 = 180
i.e. x = 180-144 = 36

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

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16 Oct 2016, 10:52
1
1
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

Attachment:
T6103.png

Each internal ∠ of a regular pentagon = 108°
So, External ∠EAF = ∠AEF = ( 180° - 108° ) => 72°

We know that in a triangle sum of the three internal angles is = 180°

Hence, ∠EAF + ∠AEF + x° = 180°

Or, 72° + 72° + x° = 180°

Or, x° = 36°

Hence correct answer will be (A) 36°
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Joined: 05 Mar 2015
Posts: 1001
Re: If ABCDE is a regular pentagon, what is the value of x in the figure a  [#permalink]

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16 Oct 2016, 11:53
1
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

Attachment:
The attachment T6103.png is no longer available

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T6103.png [ 14.23 KiB | Viewed 2509 times ]

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

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20 Oct 2018, 02:10
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Re: If ABCDE is a regular pentagon, what is the value of x in the figure a   [#permalink] 20 Oct 2018, 02:10
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