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# Which of the following could be a value of x, in the diagram above?

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Re: Which of the following could be a value of x, in the diagram above? [#permalink]
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Bunuel wrote:

Which of the following could be a value of x, in the diagram above?

A. 10
B. 20
C. 40
D. 50
E. any of the above

Attachment:
p002-1.gif

5x=D+C
or,
5x=90 +C
or,
5x > 90
substituting x = 10 , 5x =50 < 90
now x cannot take values 40 or 50 because that will make 5x > 180
the only option left is 20 , so B
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Re: Which of the following could be a value of x, in the diagram above? [#permalink]
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A. 10
B. 20
C. 40
D. 50
E. any of the above

SOLVING BY ANS CHOICE

A) 10 WHEN X IS 10 5X = 50 AND SINCE 5X IS ON A STRAIGHT LINE 5X +dbc = 180 THERFORE IT MEANS DBC = 180-50 = 130 BUT THAT CANNOT BE AS ONE ANGLE OF THE TRIANGLE IS ALREADY 90 THERFORE A = RULED OUT.

B) X=20 MEans 5x = 100 and angle dbc = 80 therefore 90+80+10 = 180 possible
c) x=40 means 5x= 200 not possible as both angle on a straight line max can be 180
d) x=50 mens 5x=250 not possible as both angle on a straight line = 180 thefore ans = b
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Re: Which of the following could be a value of x, in the diagram above? [#permalink]
Bunuel wrote:

Which of the following could be a value of x, in the diagram above?

A. 10
B. 20
C. 40
D. 50
E. any of the above

Attachment:
p002-1.gif

Angle B = 180 - 5x

We know that in triangle BDC, angle B is greater than 0 and less than 90 (Since angle D = 90 in triangle BDC)

—> B > 0
—> 180 - 5x > 0
—> 5x < 180
—> x < 36

And B < 90 in triangle BCD
—> 180 - 5x < 90
—> 180 - 90 < 5x
—> 5x > 90
—> x > 18

So 18 < x < 38

Only 1 Option satisfies = 20 degrees

IMO Option B

Pls Hit kudos if you like the solution

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Re: Which of the following could be a value of x, in the diagram above? [#permalink]
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Re: Which of the following could be a value of x, in the diagram above? [#permalink]
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