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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If AD = BC, find the value of x
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Updated on: 02 Apr 2022, 10:50
Updated on: 02 Apr 2022, 10:50
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Question Stats:
26% (02:42) correct
73% (02:22) wrong based on 46 sessions
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AD = BC
∠ABC = 90°
Quantity A |
Quantity B |
x |
30 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Originally posted by GreenlightTestPrep on 28 Jan 2021, 09:55.
Last edited by Carcass on 02 Apr 2022, 10:50, edited 1 time in total.
Last edited by Carcass on 02 Apr 2022, 10:50, edited 1 time in total.
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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If AD = BC, find the value of x
[#permalink]
28 Jan 2021, 10:02
28 Jan 2021, 10:02
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4
Bookmarks
GreenlightTestPrep wrote:
AD = BC
∠ABC = 90°
Quantity A |
Quantity B |
x |
30 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Important: Even though we aren't provided any angles, we can still label many of the angles in the diagram.
Since angles on a line must add to 180°, ∠ADB = (180 - 2x)°
Since angles in ∆ADB must add to 180°, ∠BAD = x°
Since ∆ADB has two equal angles (of x°), the triangle is an isosceles triangle which means side BD = side AD
Since side BD = side BC, we have an isosceles triangle which means ∠DCB = 2x°, and since all angles must add to 180 degrees, we can see that ∠DBC = (180 - 4x)°
Finally, since ∠ABC = 90°, we can write: x + (180 - 4x)° = 90°
Simplify: 180 - 3x = 90
Solve: x = 30
We get:
QUANTITY A: 30
QUANTITY B: 30
Answer: C
Cheers,
Brent
General Discussion
Re: If AD = BC, find the value of x
[#permalink]
28 Jan 2021, 11:24
28 Jan 2021, 11:24
2
Hi, I am a bit confused here, hope you guys can help :
What if I start with angle DBC = 90-x, then
2x+90-x+dcb = 180
dcb = 90-x
this will make DB=DC
and then if i continue, I get x = 60
Please help guys
What if I start with angle DBC = 90-x, then
2x+90-x+dcb = 180
dcb = 90-x
this will make DB=DC
and then if i continue, I get x = 60
Please help guys
