GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Jul 2020, 07:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A regular polygon is inscribed in a circle. If 3 of the inscribed

Author Message
TAGS:

### Hide Tags

SC Moderator V
Joined: 25 Sep 2018
Posts: 871
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

### Show Tags

3 00:00

Difficulty:   45% (medium)

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

### HideShow timer Statistics

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

_________________
Senior Manager  G
Joined: 25 Feb 2019
Posts: 331
Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

### Show Tags

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
VP  V
Joined: 27 May 2012
Posts: 1067
Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

### Show Tags

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.
_________________
- Stne
Senior Manager  G
Joined: 25 Feb 2019
Posts: 331
Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

### Show Tags

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

Posted from my mobile device
SC Moderator V
Joined: 25 Sep 2018
Posts: 871
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

### Show Tags

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
_________________
SC Moderator V
Joined: 25 Sep 2018
Posts: 871
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

### Show Tags

stne i hope the above solution helps you understand better _________________
Director  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 950
WE: Supply Chain Management (Energy and Utilities)
A regular polygon is inscribed in a circle. If 3 of the inscribed  [#permalink]

### Show Tags

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)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine A regular polygon is inscribed in a circle. If 3 of the inscribed   [#permalink] 07 May 2019, 23:43

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