• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 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 PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the value of x in the figure? tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## What is the value of x in the figure? 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. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 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

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

GMAT Instructor
Joined
04 Oct 2017
Posted:
551 messages
Followed by:
11 members
180
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.

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.
• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

### 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 Scott@TargetTestPrep

Target Test Prep

199 posts
2 Max@Math Revolution

Math Revolution

84 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 Ian Stewart

GMATiX Teacher

65 posts
5 GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts