GMAT Changed on April 16th - Read about the latest changes here

 It is currently 26 May 2018, 08:39

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In a polygon with 9 equal sides and 9 equal angles

Author Message
TAGS:

### Hide Tags

Intern
Joined: 25 Mar 2013
Posts: 3
Location: Italy
WE: General Management (Other)
In a polygon with 9 equal sides and 9 equal angles [#permalink]

### Show Tags

02 Apr 2013, 10:25
1
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:08) correct 42% (01:13) wrong based on 137 sessions

### HideShow timer Statistics

In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

_________________

Labor omnia vincit

Math Expert
Joined: 02 Sep 2009
Posts: 45440
Re: In a polygon with 9 equal sides and 9 equal angles [#permalink]

### Show Tags

02 Apr 2013, 10:31
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
matspring wrote:
In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

The # of diagonals in $$n$$ sided polygon equals to $$C^2_n-n=\frac{n(n-3)}{2}$$: $$C^2_n$$ choose any two vertices out of $$n$$ points to connect minus $$n$$ sides, which won't be diagonals.

So, # of diagonals in 9 sided polygon is $$\frac{n(n-3)}{2}=27$$.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 45440
Re: In a polygon with 9 equal sides and 9 equal angles [#permalink]

### Show Tags

02 Apr 2013, 10:33
1
KUDOS
Expert's post
matspring wrote:
In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

Similar question to practice: how-many-diagonals-does-a-polygon-with-21-sides-have-if-one-101540.html

Hope it helps
_________________
Intern
Joined: 14 Jun 2012
Posts: 28
Concentration: Strategy, Technology
Schools: Goizueta '15 (D)
GMAT 1: 640 Q47 V32
GMAT 2: 640 Q47 V32
GMAT 3: 730 Q49 V40
WE: Information Technology (Computer Software)
Re: In a polygon with 9 equal sides and 9 equal angles [#permalink]

### Show Tags

02 Apr 2013, 10:36
3
KUDOS
2
This post was
BOOKMARKED
matspring wrote:
In a polygon with 9 equal sides and 9 equal angles, how many different diagonals can be drawn ?

(A) 18
(B) 27
(C) 36
(D) 54
(E) 72

The OA should be (B), however I'm not sure 100% about it; this exercise belong to a set of problem given to me by a friend for training.

To find the number of diagonals in a polygon with n sides, use the following formula:
n (n-3) / 2.

9*6/2 = 27.

Here’s where the diagonal formula comes from and why it works. Each diagonal connects one point to another point in the polygon that isn’t its next-door neighbor. In an n-sided polygon, you have n starting points for diagonals. And each diagonal can go to (n – 3) ending points because a diagonal can’t end at its own starting point or at either of the two neighboring points. So the first step is to multiply n by (n – 3). Then, because each diagonal’s ending point can be used as a starting point as well, the product n(n – 3) counts each diagonal twice. That’s why you divide by 2.

http://www.dummies.com/how-to/content/h ... lygon.html
Non-Human User
Joined: 09 Sep 2013
Posts: 6855
Re: In a polygon with 9 equal sides and 9 equal angles [#permalink]

### Show Tags

09 Nov 2017, 10:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In a polygon with 9 equal sides and 9 equal angles   [#permalink] 09 Nov 2017, 10:38
Display posts from previous: Sort by