• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Regular polygon X has r sides, and each vertex has...

This topic has 1 expert reply and 0 member replies

Regular polygon X has r sides, and each vertex has...

Post Sun Nov 05, 2017 4:53 pm
Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q?

A. 2
B. 160
C. 176
D. 178
E. 179

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

GMAT/MBA Expert

Post Tue Nov 07, 2017 5:44 pm
LUANDATO wrote:
Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of polygon Q?

A. 2
B. 160
C. 176
D. 178
E. 179

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
If we want to find the maximum possible angle measure for the interior angles of Q, we first need to find the max possible angle measure for X, as Q will have 1/4 as many sides as X.

Equation for finding the sum of all interior angles of a polygon with 'n' sides: (n-2) * 180
Equation for finding the measure of each interior angle of a regular polygon with 'n' sides: (n-2)*180/n

If the interior angles of X are integer values, then the greatest possible measure of each angle would be 179 degrees. (180 would be a straight line, and thus not a polygon.)
To find the number of sides of a polygon with interior angles of 179, simply set the above equation to 179:
(n-2)*180/n = 179
(n-2) *180 = 179n
180n - 360 = 179n
-360 = -n
n = 360

So X can have at most 360 sides.

If Q has 1/4 the number of sides as X, then Q, at most, can have 360/4= 90 sides.
If n = 90, each interior angle would be (90-2)*180/90 = 88*180/90 = 88*2 = 176. The answer is C

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

Best Conversation Starters

1 Roland2rule 174 topics
2 lheiannie07 110 topics
3 ardz24 64 topics
4 LUANDATO 56 topics
5 swerve 46 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

150 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

145 posts
3 image description Rich.C@EMPOWERgma...

EMPOWERgmat

116 posts
4 image description GMATGuruNY

The Princeton Review Teacher

103 posts
5 image description Scott@TargetTestPrep

Target Test Prep

98 posts
See More Top Beat The GMAT Experts