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If in the figure above, ABCD is a parallelogram and ADEF is a rectangl

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If in the figure above, ABCD is a parallelogram and ADEF is a rectangl  [#permalink]

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New post 09 Sep 2018, 09:05
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If in the figure above, ABCD is a parallelogram and ADEF is a rectangle such that AB = AF, then what is the value of x - y ?


A. 10°
B. 50°
C. 90°
D. 100°
E. 115°


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image060.jpg
image060.jpg [ 2.9 KiB | Viewed 416 times ]

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Re: If in the figure above, ABCD is a parallelogram and ADEF is a rectangl  [#permalink]

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New post 09 Sep 2018, 09:35
Bunuel wrote:
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If in the figure above, ABCD is a parallelogram and ADEF is a rectangle such that AB = AF, then what is the value of x - y ?


A. 10°
B. 50°
C. 90°
D. 100°
E. 115°


Attachment:
image060.jpg


Angle ADC=40
x=140= Angle BAD [Since ABCD is a parallelogram, opposite angles are equal]
AB=AF
Angle AFB=ABF=y
Angle BAF = 360-(140+90) [ADEF is a rectangle so each angle is 90]
= 360-230=130
In triangle ABF, 2y+130=180
y=25
x-y=140-25=115
Answer E.
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Re: If in the figure above, ABCD is a parallelogram and ADEF is a rectangl  [#permalink]

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New post 09 Sep 2018, 09:40
Bunuel wrote:
Image
If in the figure above, ABCD is a parallelogram and ADEF is a rectangle such that AB = AF, then what is the value of x - y ?


A. 10°
B. 50°
C. 90°
D. 100°
E. 115°


x=180-40=40 (Consecutive angles of a parallelogram are supplementary)
Angle BAD=x=140 (Opposite angels of a parallelogram are congruent)

In the isosceles triangle ABF, Angle A=360-90-140=130
So, \(y=\frac{(180-130)}{2}\)=25

So, x-y=140-25=115°

Ans. (E)
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Re: If in the figure above, ABCD is a parallelogram and ADEF is a rectangl  [#permalink]

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New post 09 Sep 2018, 10:34
Angle BCD (x)=140 as,
180 - Angle ABC = 140

Angle BAD = 180- Angle ABC
=140

Angle FAD is 90
Therefore, Angle BAF = 360 - Angle FAD + Angle BAD
=130
Since,
AB=AF
Angle AFB=ABF=y
2y = 50
y=25


x-y=140-25=115


Ans is E
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Re: If in the figure above, ABCD is a parallelogram and ADEF is a rectangl  [#permalink]

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New post 09 Sep 2018, 12:28
If in the figure above, ABCD is a parallelogram and ADEF is a rectangle such that AB = AF, then what is the value of x - y ?


A. 10°
B. 50°
C. 90°
D. 100°
E. 115°

Answer is E.

In the parallelogram, opposite sides are equal, and the total sum of all the angles is 360, so we get x to be 140.
the triangle is an isosceles triangle and thus one side will be 90+140=230,and 360-230=130, ,also sum of all sides in a triangle is 180 so y=25,

Questions asks x-y=140-25=115.

Option E.
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Re: If in the figure above, ABCD is a parallelogram and ADEF is a rectangl  [#permalink]

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New post 09 Sep 2018, 18:06
In the parallelogram, opposite angles are equal, that means Angle ABC=ADC=40
which means other two are also equal comes to Angle BAC=BCD=x=140 (Sum of the angles in a quadrilateral is 360)

In the traingle above, AB=AF which means opposite angles are also equal.
Angle ABF=AFB=y

In Traingle ABF, Angle BAF=360-90-140 which comes to 130.
then y=25

x-y=140-25=115
Re: If in the figure above, ABCD is a parallelogram and ADEF is a rectangl &nbs [#permalink] 09 Sep 2018, 18:06
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