• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

What is the value of x in the figure?

This topic has 2 expert replies and 0 member replies

What is the value of x in the figure?

Post


If ABCDE is a regular pentagon, what is the value of x in the figure above?

A. 36
B. 42
C. 45
D. 48
E. 72

The OA is A.

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

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
122 members
Upvotes:
1153
GMAT Score:
770
Post
AAPL wrote:


If ABCDE is a regular pentagon, what is the value of x in the figure above?

A. 36
B. 42
C. 45
D. 48
E. 72

The OA is A.

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.
The total degrees of a polygon with n sides is (n-2)* 180.
Total degrees in a pentagon = (5-2)*180 = 3*180 = 540.
If all the angles are equal (as they are in a regular pentagon), then each angle is 540/5 = 108.

Now we know that the angles FEA and FAE will each be 180-108 = 72. If we have two angles measuring 72 degrees, which will sum to 144 degrees, we know the remaining angle will be 180-144 = 36. The answer is A

_________________
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!

GMAT/MBA Expert

Post
Quote:
If ABCDE is a regular pentagon, what is the value of x in the figure above?

A. 36
B. 42
C. 45
D. 48
E. 72

The OA is A.

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.
Hi AAPL,
Let's take a look at your question.

ABCDE is a regular pentagon. We know that we can calculate the sum of interior angles of a regular polygon using the formula:
$$\left(n-2\right)\times180^o$$
Where n is the number of sides of the polygon.

For a regular pentagon n = 5.
Therefore, sum of interior angles of a pentagon will be:
$$=\left(5-2\right)\times180^o$$
$$=\left(3\right)\times180^o=540^o$$

Since there are five angles inside the pentagon, we can calculate the measure of each angle as:
$$=\frac{540^o}{5}=108^o$$

Now we can find the interior angles of the triangle FAE.
$$m\angle FEA=180^o-m\angle DEA$$
$$m\angle FEA=180^o-108^o=72^o$$

Similarly,
$$m\angle FAE=180^o-m\angle BAE$$
$$m\angle FAE=180^o-108^o=72^o$$

Now we can find the value of x.
We know that sum of interior angles of a triangle is 180 degree, therefore,

$$x^o=180^o-m\angle FEA-m\angle FAE$$
$$x^o=180^o-72^o-72^o$$
$$x^o=36^o$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test 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
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • 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
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts