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If AD = DB, DC = CB, and angle ABC = 90º as shown above, then what is the value of xº?
A. 40º
B. 50º
C. 65º
D. 80º
E. 100º
Attachment:
1.png [ 6.31 KiB | Viewed 2570 times ]
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Bunuel
In isos triangle BDC:
2x + 100 = 180
2x = 80
x = 40
So, DBC = 90 - 40 = 50
x = 50(Why? triangle BAD is isos)
IMO, (B)!
Posts: 1,052
Explanation:
In Triangle DBC,
DC=CB, Angle CDB = Angle DBC =y
Angle C = 100
Angle CDB + Angle DBC + Angle C = 180
2y + 100 = 180
y = 40
We know, Angle ABC is 90
Angle DBA = 90-40 = 50
Angle DBA = Angle DAB = 50
IMO-B
Posted from my mobile device
In Triangle DBC,
DC=CB, Angle CDB = Angle DBC =y
Angle C = 100
Angle CDB + Angle DBC + Angle C = 180
2y + 100 = 180
y = 40
We know, Angle ABC is 90
Angle DBA = 90-40 = 50
Angle DBA = Angle DAB = 50
IMO-B
Posted from my mobile device
DAB = DBA = x
Triangle DCB has angles of 40, 40, 100.
So, x + 40 = 90 => x = 50 (B)
Triangle DCB has angles of 40, 40, 100.
So, x + 40 = 90 => x = 50 (B)
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)
AD = DB, DC = CB, and angle ABC = 90º as shown above, then what is the value of xº
In triangle CBD,
CD = CB
angle CDB = angle CBD (isosceles triangle)
100 +2y = 180
2y = 80
y=40
In triangle ABD,
AD = BD
angle DAB = angle DBA
Also given
angle CBA = 90
angle DBA = 90 -40 =50
x = 50
IMO B
In triangle CBD,
CD = CB
angle CDB = angle CBD (isosceles triangle)
100 +2y = 180
2y = 80
y=40
In triangle ABD,
AD = BD
angle DAB = angle DBA
Also given
angle CBA = 90
angle DBA = 90 -40 =50
x = 50
IMO B
Two equal angles in Triangle BDC are \(\frac{(180-100)}{2} = 40\)
X= 90 - 40 = 50
Option B
X= 90 - 40 = 50
Option B
Bunuel
Posts: 731
Bunuel
Simply fill the angle to find x: IMO B
Follow the diagram
Attachments
PB07.PNG [ 8.23 KiB | Viewed 2213 times ]
GMAT 1: 760 Q51 V42
Posts: 10,057
In triangle DCB, since DC = CB, therefore angle CDB = angle CBD = 40 (sum of all angles in the traingle is 180)
Angle B is 90 hence and angle CBD is 40 so angle DBA is 90 - 40 = 50.
Since AD = DB, therefore angle DAB = angle DBA = 50 (angle opposite to equal sides are equal)
Therefore, x = 50
Answer B
Angle B is 90 hence and angle CBD is 40 so angle DBA is 90 - 40 = 50.
Since AD = DB, therefore angle DAB = angle DBA = 50 (angle opposite to equal sides are equal)
Therefore, x = 50
Answer B
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