GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Feb 2020, 18:52 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If O is the center of the circle shown above, what is the measure of x

Author Message
TAGS:

### Hide Tags

Retired Moderator Joined: 29 Apr 2015
Posts: 807
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
If O is the center of the circle shown above, what is the measure of x  [#permalink]

### Show Tags

1
1
15 00:00

Difficulty:   55% (hard)

Question Stats: 61% (01:47) correct 39% (02:18) wrong based on 132 sessions

### HideShow timer Statistics

Attachment: E89063a.png [ 7.38 KiB | Viewed 2586 times ]
If O is the center of the circle shown above, what is the measure of x?

A. 30°
B. 40°
C. 50°
D. 80°
E. 100°

Attachment: E89063c.png [ 9.79 KiB | Viewed 2572 times ]
Veritas Prep GMAT Instructor Joined: 23 Oct 2013
Posts: 144
Re: If O is the center of the circle shown above, what is the measure of x  [#permalink]

### Show Tags

This is a pretty simple question that relies on the central angle and inscribed angle rules of circles. For inscribed angles (angles coming from the side of a circle), simply double them and then treat them as central angles. Here we have a central angel of 100 degrees as well as a diameter of the circle given to us. This means that the other portion of the arc on that semicircle above the diameter is 80 degrees (180-100 = 80). Because x is an inscribed angle covering that entire 80 degree portion, we use the inscribed angle rule in reverse. If the angles covers what would be 80 degrees of a central angle, then we divide that in half to reach the inscribed angle of 40 degrees, or answer choice B.

I hope this helps!
Senior Manager  Joined: 07 Aug 2011
Posts: 492
GMAT 1: 630 Q49 V27
Re: If O is the center of the circle shown above, what is the measure of x  [#permalink]

### Show Tags

4
reto wrote:
Attachment:
The attachment E89063a.png is no longer available
If O is the center of the circle shown above, what is the measure of x?

A. 30°
B. 40°
C. 50°
D. 80°
E. 100°

Attachments gmatclub.jpg [ 25.39 KiB | Viewed 2496 times ]

Manager  B
Joined: 15 Nov 2017
Posts: 51
Re: If O is the center of the circle shown above, what is the measure of x  [#permalink]

### Show Tags

Could someone provide more insight about the rules related to this problem? I am having trouble correctly solving this one. Thank you!

reto wrote:
Attachment:
E89063a.png
If O is the center of the circle shown above, what is the measure of x?

A. 30°
B. 40°
C. 50°
D. 80°
E. 100°
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3706
If O is the center of the circle shown above, what is the measure of x  [#permalink]

### Show Tags

1
KHow wrote:
Could someone provide more insight about the rules related to this problem? I am having trouble correctly solving this one. Thank you!

reto wrote:
Attachment:
The attachment E89063a.png is no longer available
If O is the center of the circle shown above, what is the measure of x?

A. 30°
B. 40°
C. 50°
D. 80°
E. 100°

Attachment: inscribed angles 2019.1.17.png [ 39.99 KiB | Viewed 909 times ]

KHow , sure.
One central angle and one inscribed angle intercept the same arc, in my diagram, arc AB
Central angle measure yields arc measure
Arc measure yields inscribed angle measure $$= x$$

A central angle is formed by two radii, OA and OB with its vertex at center O

• degree measure of central angle ∠ AOB
Straight line = 180°
Two angles that lie on a straight line sum to 180°
100° + ∠AOB = 180°
∠ AOB = 80°

1) ∠ AOB is "subtended" by arc AB, or ∠ AOB intercepts arc AB

2) degree measure of intercepted arc AB ?

The radii of sector AOB intercept the circumference of the circle and create arc AB.

We cam also say that ∠ AOB "subtends" arc AB

Rule: The length of an arc subtended by a central angle has the same degree measure as the central angle

∠ AOB = 80°

Because ∠ AOB is a central angle, arc AB also = 80°

3) from degree measure of arc AB, find inscribed ∠ ACB measure = $$x$$

An inscribed angle is formed by two intersecting chords, AC and BC, whose vertex lies on the circumference of the circle

4) An inscribed angle has a degree measure that is $$\frac{1}{2}$$ that of the arc it intercepts

Rule: the degree measure of an inscribed angle is half that of the arc that the angle intercepts

5) arc AB = 80°

6) x =?
∠ ACB = $$x = \frac{1}{2}$$ of arc AB

$$x = \frac{1}{2} * 80°$$

$$x = 40°$$

Hope that helps.

This site, here, and this site, here discuss the relationship between and among inscribed angles, central angles, and intercepted arcs
_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has. -- Margaret Mead
Manager  B
Joined: 15 Nov 2017
Posts: 51
Re: If O is the center of the circle shown above, what is the measure of x  [#permalink]

### Show Tags

1
This is VERY helpful. Finally get it. Thanks a lot! generis wrote:
KHow wrote:
Could someone provide more insight about the rules related to this problem? I am having trouble correctly solving this one. Thank you!

reto wrote:
Attachment:
E89063a.png
If O is the center of the circle shown above, what is the measure of x?

A. 30°
B. 40°
C. 50°
D. 80°
E. 100°

Attachment:
inscribed angles 2019.1.17.png

KHow , sure.
One central angle and one inscribed angle intercept the same arc, in my diagram, arc AB
Central angle measure yields arc measure
Arc measure yields inscribed angle measure $$= x$$

A central angle is formed by two radii, OA and OB with its vertex at center O

• degree measure of central angle ∠ AOB
Straight line = 180°
Two angles that lie on a straight line sum to 180°
100° + ∠AOB = 180°
∠ AOB = 80°

1) ∠ AOB is "subtended" by arc AB, or ∠ AOB intercepts arc AB

2) degree measure of intercepted arc AB ?

The radii of sector AOB intercept the circumference of the circle and create arc AB.

We cam also say that ∠ AOB "subtends" arc AB

Rule: The length of an arc subtended by a central angle has the same degree measure as the central angle

∠ AOB = 80°

Because ∠ AOB is a central angle, arc AB also = 80°

3) from degree measure of arc AB, find inscribed ∠ ACB measure = $$x$$

An inscribed angle is formed by two intersecting chords, AC and BC, whose vertex lies on the circumference of the circle

4) An inscribed angle has a degree measure that is $$\frac{1}{2}$$ that of the arc it intercepts

Rule: the degree measure of an inscribed angle is half that of the arc that the angle intercepts

5) arc AB = 80°

6) x =?
∠ ACB = $$x = \frac{1}{2}$$ of arc AB

$$x = \frac{1}{2} * 80°$$

$$x = 40°$$

Hope that helps.

This site, here, and this site, here discuss the relationship between and among inscribed angles, central angles, and intercepted arcs
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9461
Location: United States (CA)
Re: If O is the center of the circle shown above, what is the measure of x  [#permalink]

### Show Tags

reto wrote:
Attachment:
E89063a.png
If O is the center of the circle shown above, what is the measure of x?

A. 30°
B. 40°
C. 50°
D. 80°
E. 100°

Attachment:
E89063c.png

The arc corresponding to angle x is 360 - 180 - 100 = 80 degrees. Since angle x is an inscribed angle, it’s equal to 80/2 = 40 degrees.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If O is the center of the circle shown above, what is the measure of x   [#permalink] 18 Jan 2020, 04:20
Display posts from previous: Sort by

# If O is the center of the circle shown above, what is the measure of x  