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

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
The pentagon ABCDE is inscribed in a circle with center O. How many de [#permalink]

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29 Oct 2017, 02:01
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25% (medium)

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79% (00:42) correct 21% (01:02) wrong based on 55 sessions

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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 [ 11.88 KiB | Viewed 1260 times ]
[Reveal] Spoiler: OA

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

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29 Oct 2017, 08:29
Bunuel wrote:

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

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

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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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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.

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

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