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05 Jul 2021, 01:30
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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 3042 times ]
asishron29181
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Given Kudos: 68
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
05 Jul 2021, 02:34
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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
05 Jul 2021, 03:09
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ABC and ADC are isosceles right angled triangle; Hence, X = 90 degrees
Bunuel
