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# A regular polygon is inscribed in a circle. If 3 of the inscribed

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A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

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03 May 2019, 08:21
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45% (medium)

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61% (01:46) correct 39% (02:19) wrong based on 38 sessions

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A regular polygon is inscribed in a circle. If 3 of the inscribed consecutive angles correspond to an arc angle measurement of 108°, how many sides are in the inscribed polygon?
A) 12
B) 10
C)9
D)8
E)6

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Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

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03 May 2019, 08:27
IMO B

the 3 inscribed angles correspond to 108

then each corresond to 36
now total sum can be 360

so sides = 360/36 = 10

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Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

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07 May 2019, 03:05
m1033512 wrote:
IMO B

the 3 inscribed angles correspond to 108

then each corresond to 36
now total sum can be 360

so sides = 360/36 = 10

Posted from my mobile device

Hi m1033512,
Can you clarify further, not sure about above.
You have solved assuming the sum of interior angles of the polygon to be 360.
sum of interior angles is given by (n-2)*180 , if this equals 360 then n should be 4 .

Thank you.
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- Stne
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Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

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07 May 2019, 04:04
Not interior angles,

360 = sum of angles subtended at the center by the arcs

so three consecutive subtended 108

each subtended 36

so total side = 360/36 = 10

hope this helps

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Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

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07 May 2019, 10:39
Solution:
Since the polygon is regular, it must have all equal angles, with this we can set up to calculate the number of sides of the polygon
$$\frac{3 angles}{108 degree}$$=$$\frac{x angles}{360 degree}$$
$$\frac{1}{36}$$ = $$\frac{x}{360}$$ i.e x= $$\frac{360}{36}$$
x= 10
If the polygon has 10 angles, it also has 10 sides
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Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

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07 May 2019, 10:39
stne i hope the above solution helps you understand better
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A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

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07 May 2019, 23:43
Abhi077 wrote:
A regular polygon is inscribed in a circle. If 3 of the inscribed consecutive angles correspond to an arc angle measurement of 108°, how many sides are in the inscribed polygon?
A) 12
B) 10
C)9
D)8
E)6

Concept:-

1) The sum of all the angles of a inscribed regular polygon corresponds to an arc measurement of 360 degree.
2) All the angles of a regular polygon are equal.

Hence, Each of the internal angle of the polygon corresponds to an arc measurement angle=108/3=36 degree

So , 36* no of angles at the center of the circle=360 degree
Or, no of angles at the center of the circle=360/36=10
Or, The no of sides of the polygon=10

Ans. (B)
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A regular polygon is inscribed in a circle. If 3 of the inscribed   [#permalink] 07 May 2019, 23:43