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

 It is currently 05 Aug 2020, 14:38

### 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 AB = BC, DA = AC, and angles DCB and ABC are right angles as shown

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65808
If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown  [#permalink]

### Show Tags

08 Jul 2020, 03:18
00:00

Difficulty:

15% (low)

Question Stats:

89% (01:04) correct 11% (01:13) wrong based on 65 sessions

### HideShow timer Statistics

If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

A. 30º
B. 45º
C. 60º
D. 90º
E. 105º

Project PS Butler

Attachment:

_________________
PS Forum Moderator
Joined: 18 Jan 2020
Posts: 1533
Location: India
GPA: 4
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown  [#permalink]

### Show Tags

08 Jul 2020, 03:23
1
AB = BC and B = 90°
ABC is a 90°,45°,45° right angle triangle.
Similarly Angle C is a 90° angle, consisting of two angles BCA and ACD. 45° and 45° each

Hence angle A is 90° (180-45-45)

Posted from my mobile device
Senior Manager
Joined: 01 Mar 2015
Posts: 294
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown  [#permalink]

### Show Tags

08 Jul 2020, 03:28
Bunuel wrote:

If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

A. 30º
B. 45º
C. 60º
D. 90º
E. 105º

BAC = BCA (Angles opp to equal sides are equal)
BAC + BCA + 90 = 180
=> BCA = 45º = BAC

ACD = 90º - BCA = 45º
ACD = ADC = 45º (Angles opp to equal sides are equal)
x + ACD + ADC = 180º
=> X = 180º - 90º = 90º

Hence, OA is (D)
GMAT Club Legend
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A motivator and an Optimist :)
Joined: 08 Jul 2010
Posts: 4521
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown  [#permalink]

### Show Tags

08 Jul 2020, 03:33
1
Bunuel wrote:

If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

A. 30º
B. 45º
C. 60º
D. 90º
E. 105º

Project PS Butler

Attachment:

Angle D = Angle ACD $$= \frac{(180-x)}{2}$$

Angle DAB = x+45º

Sum of all angles of Trapezium ABCD = 360º

i.e. Angle D + Angle DAB = 360-(90+90) = 180

i.e. $$\frac{(180-x)}{2}$$ + $$x+45º$$ $$= 180$$

i.e. 180-x+2x = 2*135º

i.e. x = 90º

_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Manager
Joined: 11 May 2019
Posts: 138
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown  [#permalink]

### Show Tags

08 Jul 2020, 03:39
1
IMO D.

AC bisects 90 angle .
Therefore in triangle ACD angle C and angle D are same (45) (because of equal sides)

x + 45 + 45 =180.

x is 90.

Posted from my mobile device
Manager
Joined: 17 Jun 2020
Posts: 126
Location: India
Concentration: Marketing, Sustainability
GMAT 1: 480 Q34 V20
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown  [#permalink]

### Show Tags

08 Jul 2020, 03:57
If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

A. 30º
B. 45º
C. 60º
D. 90º
E. 105º

ABC is a isosceles right angle triangle so Angle B = 90. Angle BCA and BAC= 45.
Angle DCB is 90 (given)
But DCB = DCA + BCA = 90= 45+ DCA….
so DCA = 45 and hence angle ADC = 45.
Using the sum of the angles of a triangle we get
ADC + DAC + ACD = 180
180 = 2 (45) = DAC = 180-90= 90

OA D
Manager
Joined: 11 Mar 2012
Posts: 178
Location: India
Concentration: General Management, Marketing
GMAT 1: 600 Q50 V22
GPA: 3.48
WE: Project Management (Real Estate)
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown  [#permalink]

### Show Tags

08 Jul 2020, 19:27
1
Bunuel wrote:

If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

A. 30º
B. 45º
C. 60º
D. 90º
E. 105º

Project PS Butler

Attachment:

As Triangle ABC is an isosceles right angle triangle - Angle ACB = 45 degrees.
And given that Angle C - 90 degrees
Angle ACD will be 90 - 45 = 45 degrees

And as Triangle ACD is also an isosceles triangle and AC = AD
Angle ACD = Angle ADC = 45 degrees.

Hence Angle x = 180-45-45 = 90 degrees.

OA: D
_________________
Top Scorer of SP Jain Global's SPJAT with above 99 percentile score

Aiming for a real big thing through GMAT
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown   [#permalink] 08 Jul 2020, 19:27