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# If O is the center of the circle above, what fraction of the circular

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Math Expert
Joined: 02 Sep 2009
Posts: 59622
If O is the center of the circle above, what fraction of the circular  [#permalink]

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13 Aug 2019, 03:28
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Difficulty:

35% (medium)

Question Stats:

65% (01:09) correct 35% (01:30) wrong based on 82 sessions

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If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

A. 1/36
B. 1/12
C. 1/9
D. 1/6
E. The answer cannot be determined from the given information.

Attachment:

image496.png [ 4.46 KiB | Viewed 813 times ]

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Re: If O is the center of the circle above, what fraction of the circular  [#permalink]

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13 Aug 2019, 09:13
Bunuel wrote:

If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

A. 1/36
B. 1/12
C. 1/9
D. 1/6
E. The answer cannot be determined from the given information.

Attachment:
image496.png

If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

12x = 1
x=1/12

IMO B
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Re: If O is the center of the circle above, what fraction of the circular  [#permalink]

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26 Sep 2019, 11:26
Bunuel wrote:

If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

A. 1/36
B. 1/12
C. 1/9
D. 1/6
E. The answer cannot be determined from the given information.

Attachment:
The attachment image496.png is no longer available

The angles marked in red are vertically opposite angles hence equal. Sum of all angles = 12x

Therefore the required fraction = x/12x =1/12 (B)
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Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: If O is the center of the circle above, what fraction of the circular  [#permalink]

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04 Oct 2019, 01:37
1
Bunuel wrote:

If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

A. 1/36
B. 1/12
C. 1/9
D. 1/6
E. The answer cannot be determined from the given information.

Attachment:
image496.png

Official Explanation

In this question, the angles shown appear span half the circle. We can infer that they must, in fact, because the opposite angles of bisecting lines are equal. On the other side of each of the 2x angles shown is another 2x, and on the other side of each x shown is another x. Therefore,

2x + x + 2x + x = 180

Half the span of the circle. Thus, 6x = 180 and x = 30. Since the full span of a circle is 360 degrees, the angle x spans a fraction of 30/360 = 1/12.

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Joined: 02 Sep 2009
Posts: 59622
Re: If O is the center of the circle above, what fraction of the circular  [#permalink]

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04 Oct 2019, 01:39
Bunuel wrote:

If O is the center of the circle above, what fraction of the circular region is encompassed by an angle of x degrees?

A. 1/36
B. 1/12
C. 1/9
D. 1/6
E. The answer cannot be determined from the given information.

Attachment:
image496.png

Video Explanation

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Re: If O is the center of the circle above, what fraction of the circular  [#permalink]

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21 Nov 2019, 23:07
From the figure, the given angles make up 180 degrees.

=> 6x = 180 => x=30.

The fraction encompassed by the angle x would x/360 => 30/360 = 1/12
Re: If O is the center of the circle above, what fraction of the circular   [#permalink] 21 Nov 2019, 23:07
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