• 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 above?

This topic has 1 expert reply and 1 member reply

What is the value of x in the figure above?

Post


In the figure above O is the center of the circle and$$\angle A$$is a right angle. If AE=AB, and$$∠EAB=90º$$, and BC=CD=DE. What is the value of x?

A. 150
B. 152
C. 160
D. 164
E. 172

The OA is A.

Experts, can you assist me with this PS question please. I have no idea about how can I solve it.

I think that I can starting assuming that EB is equal to the diameter of the circle but I don't know how can I prove it.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Hello AAPL.

Let's take a look at your question.

For the Inscribed angle theorem, we have that m(EOB)=2*m(EAB)=2*90º=180º.

Now, the triangle EAB is equilateral and it has a right angle, so the m(AEB)=m(EBA)=45º. If we consider the line AO, then m(EOA)=m(BOA)=90º.

So, xº=90+yº, where yº=m(COB).

Using again the Inscribed angle theorem we have that 180º=m(EOB)=2*m(EDB), it implies that m(EDB)=90º.

Now, the triangles DCB and DCE are isosceles, and m(DEC)=m(DCE)=m(CDB)=m(DBC)=Rº.

If we look the triangle DCE we can get that Rº+Rº+Rº+m(BDE)=180º, it implies that Rº=30º.

So, m(CDE)=120º.

Finally, using the Inscribed angle theorem, we have that the complementary angle in COE satisfy that 90º+90º+yº=2*m(CDE)=2*120=240º. That is to say, yº=60º.

So we get xº= 90º + yº = 90º+60º=150º.

The correct answer is A.

I hope this explanation may help you.

You have to take care when you read it.

I'm available if you'd like a follow-up.

Regards.

_________________
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.
Master | Next Rank: 500 Posts Default Avatar
Joined
29 Nov 2017
Posted:
100 messages
Upvotes:
14
Post
AAPL wrote:


In the figure above O is the center of the circle and$$\angle A$$is a right angle. If AE=AB, and$$∠EAB=90º$$, and BC=CD=DE. What is the value of x?

A. 150
B. 152
C. 160
D. 164
E. 172

The OA is A.

Experts, can you assist me with this PS question please. I have no idea about how can I solve it.

I think that I can starting assuming that EB is equal to the diameter of the circle but I don't know how can I prove it.


The angle formed by joining the end points of a diameter to any point on the circle is 90 degrees.

Since, Angle EAB = 90 degrees, so EB is the diameter.

Hence OE = OB = OA = radius of the circle.

EB = AB (given).

Hence triangles EOA and BOA are congruent because all 3 corresponding sides of both the triangles are equal.
hence angle EOA = angle AOB
Since angle EOA + angle AOB = Angle EOB = 180 degree so Angle 2AOB = 180 degrees.
So angle AOB = 90 degrees

Similarly, OE = OD = OC = OB = radius of the circle. ED = DC = CB (given). So triangles EOD, DOC and COB are also congruent as they have corresponding sides equal.
Therfore angle BOC = angle COD = angle DOE
angle BOC + angle COD + angle DOE = 180 degrees
Therefore 3BOC = 180
or angle BOC = 60 degrees
x = Angle AOB + AngleBOC = 90 + 60 = 150 degrees.

Hence A

  • +1 Upvote Post
  • Quote
  • Flag
  • 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
  • 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
  • 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
  • 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
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Top First Responders*

1 Ian Stewart 44 first replies
2 Brent@GMATPrepNow 34 first replies
3 Scott@TargetTestPrep 32 first replies
4 Jay@ManhattanReview 31 first replies
5 GMATGuruNY 18 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

139 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

51 posts
5 image description Jay@ManhattanReview

Manhattan Review

31 posts
See More Top Beat The GMAT Experts