GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 07:00

### 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

# If O is the center and AB parallel to CD, then x=

Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Mar 2018
Posts: 206
If O is the center and AB parallel to CD, then x=  [#permalink]

### Show Tags

Updated on: 15 Mar 2018, 20:57
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:46) correct 32% (01:46) wrong based on 39 sessions

### HideShow timer Statistics

If O is the center and AB parallel to CD, then x=

(A) 40
(B) 50
(C) 60
(D) 70
(E) 80

Attachment:

Capture1.JPG [ 31.18 KiB | Viewed 1325 times ]

_________________

Originally posted by itisSheldon on 15 Mar 2018, 08:13.
Last edited by Bunuel on 15 Mar 2018, 20:57, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7969
Re: If O is the center and AB parallel to CD, then x=  [#permalink]

### Show Tags

15 Mar 2018, 08:26
itisSheldon wrote:
If O is the center and AB parallel to CD, then x=
Attachment:
The attachment Capture1.JPG is no longer available

(A) 40
(B) 50
(C) 60
(D) 70
(E) 80

Now central angle DOB and angle at circumference BAD have SAME chord BD, so angle BAD = 20/2 = 10

AB ll CD so angle BAD = angle CDA =10

In triangle CED , DE is DIAMETER, so angle DCE = 90

take triangle CDx ... SUM = 180 = C+D+x=90+10+x......x=80

E
Attachments

Capture1.JPG [ 47 KiB | Viewed 1138 times ]

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3548
Re: If O is the center and AB parallel to CD, then x=  [#permalink]

### Show Tags

15 Mar 2018, 19:19
1
1
itisSheldon wrote:
If O is the center and AB parallel to CD, then x=

(A) 40
(B) 50
(C) 60
(D) 70
(E) 80

Attachment:

circlewithx.JPG [ 42.03 KiB | Viewed 1088 times ]

Another way:

• ∠ AOD = 160° (180° = straight line. ∠ BOD = 20°. (180° - 20°) = 160°

• ∆AOD has two congruent angles (opposite equal sides) that = 10°
-- ∠AOD of ∆AOD = 160°
-- Interior angle degrees remaining: (180° - 160°) = 20°, which must be split between two congruent angles
-- The triangle has two equal sides, both radii. Side AO = OD
-- Angles opposite equal sides are equal

• The hypotenuse of inscribed ∆CDE is the circle's diameter. Hence it is a right triangle.
-- ∠ C = 90°

• ∠BAD = ∠CDA - they are alternate interior angles of parallel lines cut by a transversal
-- AB || CD
-- the transversal is line segment AD
-- ∠BAD = 10° = ∠CDA = 10°

x = 80. It is the third angle of ∆CDF
The two known angles, in degrees, measure 90 and 10
90° + 10° = 100°
(180° - 100°) = 80°

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Re: If O is the center and AB parallel to CD, then x=   [#permalink] 15 Mar 2018, 19:19
Display posts from previous: Sort by