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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
Attachment:
1.png [ 3.08 KiB | Viewed 3137 times ]
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asishron29181
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
Given,
AB = BC, DA = AC, and angles DCB and ABC are right angles
Now angle ABC = 90
and AB = BC
which implies, angle BAC = BCA = 45
angle DCB = 90
angle ACD + angle ACB = 90
angle ACD =45
Now we also know that AD = AC
which implies angle ADC =45
x + 45 + 45 = 180
x =90
IMO D
AB = BC, DA = AC, and angles DCB and ABC are right angles
Now angle ABC = 90
and AB = BC
which implies, angle BAC = BCA = 45
angle DCB = 90
angle ACD + angle ACB = 90
angle ACD =45
Now we also know that AD = AC
which implies angle ADC =45
x + 45 + 45 = 180
x =90
IMO D
ABC and ADC are isosceles right angled triangle; Hence, X = 90 degrees
Bunuel
Quote:
Answer D:
<BAC=<BCA=45
<BCA+<ACD=90
<ACD= 45 =<ADC
<ACD + <ADC + <DAC = 180
<DAC =90
Please hit kudos if you liked the solution! Cheers
Since triangle ABC is isoceles, angle A = angle C = 45
Since BCD is 90, then the remaining angle = 45
Since ADC is isoceles, x = 180-(45*2) = 90 D
Since BCD is 90, then the remaining angle = 45
Since ADC is isoceles, x = 180-(45*2) = 90 D
Posts: 731
Bunuel
IMO D, Follow the attachment steps.
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Attachments
IMG_20210706_130842.jpg [ 38.69 KiB | Viewed 2596 times ]
IMG_20210706_130546.jpg [ 6.42 KiB | Viewed 2599 times ]
Bunuel
Clearly, <BAC = <BCA = 45 each
<BCA = <ACD = <ADC = 40 each
x + 90 = 180
x = 90 (D), IMO!
Triangle ABC forms a isosceles right triangle since side AB and BC are equal. Hence Angle A=Angle C=(180-B)/2= (180-90)/2=45 degrees
Now in Triangle ADC, Angle C=90-45=45 degrees.
Since AD=AC Triangle ADC forms isosceles triangle with angles opposite to equal sides measuring 45 degrees each.
So angle x measures 180-(45+45)=90 degrees.
IMO option (d) is the correct answer.
Now in Triangle ADC, Angle C=90-45=45 degrees.
Since AD=AC Triangle ADC forms isosceles triangle with angles opposite to equal sides measuring 45 degrees each.
So angle x measures 180-(45+45)=90 degrees.
IMO option (d) is the correct answer.
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