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The pentagon ABCDE is inscribed in a circle with center O. How many de

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The pentagon ABCDE is inscribed in a circle with center O. How many de [#permalink]

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New post 29 Oct 2017, 02:01
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The pentagon ABCDE is inscribed in a circle with center O. How many degrees is angle ABC?

(1) The pentagon ABCDE is a regular pentagon, which means that all sides are the same length and all interior angles are the same size.
(2) The radius of the circle is 5 inches.

[Reveal] Spoiler:
Attachment:
2017-10-29_1300.png
2017-10-29_1300.png [ 11.88 KiB | Viewed 752 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135335 [0], given: 12687

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Re: The pentagon ABCDE is inscribed in a circle with center O. How many de [#permalink]

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New post 29 Oct 2017, 08:29
Bunuel wrote:
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The pentagon ABCDE is inscribed in a circle with center O. How many degrees is angle ABC?

(1) The pentagon ABCDE is a regular pentagon, which means that all sides are the same length and all interior angles are the same size.
(2) The radius of the circle is 5 inches.

[Reveal] Spoiler:
Attachment:
2017-10-29_1300.png



(1) The pentagon ABCDE is a regular pentagon, which means that all sides are the same length and all interior angles are the same size.
A regular Pentagon will have all its angles EQUAL irrespective of it is inscribed in a circle or not
so SUM of angles = \((n-2)*180=(5-2)*180=3*180\)..
each angle = \(3*\frac{180}{5} = 108\)
suff

(2) The radius of the circle is 5 inches.
Nothing much
Insuff

A
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Kudos [?]: 6103 [0], given: 121

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Re: The pentagon ABCDE is inscribed in a circle with center O. How many de [#permalink]

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New post 29 Oct 2017, 08:42
(1) The pentagon ABCDE is a regular pentagon, which means that all sides are the same length and all interior angles are equal and definite value. Sufficient

(2) The radius of the circle is 5 inches.
Not sufficient

A

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Kudos [?]: 1 [0], given: 73

The pentagon ABCDE is inscribed in a circle with center O. How many de [#permalink]

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New post 29 Oct 2017, 10:31
IMO: A

Statement 1- (n-2)*180 will give sum of all angles. Since all angles are equal we will get measure of each angle.No Need to calculate.

Statement 2: We don't know anything about Polygon, whether it's regular or not.=>Insufficient.

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Re: The pentagon ABCDE is inscribed in a circle with center O. How many de [#permalink]

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New post 02 Nov 2017, 09:44
Option 1: As we know that its regular pentagon, it has 5 sides. By applying formula to find interior angle (n-2)180/n - Where n = number of sides we can find the angle.
Sufficient.
Option 2: But just mere radius we cannot find the angle.
Insufficient.

Answer: A

Kudos [?]: 2 [0], given: 9

Re: The pentagon ABCDE is inscribed in a circle with center O. How many de   [#permalink] 02 Nov 2017, 09:44
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