If the sum of the interior angles of a regular polygon...

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

If the sum of the interior angles of a regular polygon...

by AAPL » Fri Jan 19, 2018 9:43 am

If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?

A. 10 sides
B. 8 sides
C. 12 sides
D. 9 sides
E. None of these

The OA is A.

I know that exist a formula to determine the number of sides 180(n-2) but is there another way to solve this PS question? Can any experts help, please? Thanks!

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Source: Beat The GMAT — Problem Solving | Fri Jan 19, 2018 9:43 am

BestGMATEliza: Master | Next Rank: 500 Posts; Posts: 103; Joined: Mon Jun 23, 2014 11:31 pm; Thanked: 25 times; Followed by:12 members; GMAT Score:770

by BestGMATEliza » Fri Jan 19, 2018 10:05 am

I think the easiest way to solve this problem is to use the formula:
(n-2)*180=1440
1440/180=8=n-2
Therefore n=10

Eliza Chute
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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Fri Jan 19, 2018 6:50 pm

Hi AAPL,

We're told that the sum of the interior angles of a regular polygon totals 1440 degrees. We're asked for the number of sides that the polygon has. There is one essential math rule that is required to answer this question - but there are a couple of different ways to consider the rule.

I often view the rule as "add a side, add 180 degrees"

3-sides = 180 degrees
4-sides = 360 degrees
5-sides = 540 degrees
6-sides = 720 degrees
Etc.

In this way, you just have to add 180s until you hit a total of 1440...Once you do that, you'll have the correct answer.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Feb 05, 2018 9:46 am

AAPL wrote:If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?

A. 10 sides
B. 8 sides
C. 12 sides
D. 9 sides
E. None of these

We can let n = the number of sides of the polygon and use the formula for the sum of the interior angles:

1440 = 180(n - 2)

1440 = 180n - 360

1800 = 180n

10 = n

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]