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In the figure above, AB ǁ CD, AD is not parallel to BC, and the length

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Bunuel
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In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   23 May 2020, 07:58
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In the figure above, AB ǁ CD, AD is not parallel to BC, and the lengths of AD and BC are equal. What is the value of r ?

(1) q = 60
(2) p = 90


DS21217


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A
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   23 May 2020, 09:05
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Bunuel wrote:

In the figure above, AB ǁ CD, AD is not parallel to BC, and the lengths of AD and BC are equal. What is the value of r ?

(1) q = 60
(2) p = 90


DS21217


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The attachment 1.png is no longer available


This is a tricky one!
Since AB || CD, the shaded angles are equal to each other. {alternate interior angles and vertically opposite angles}

The correct answer is (A)
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   30 May 2020, 11:26
Bunuel wrote:

In the figure above, AB ǁ CD, AD is not parallel to BC, and the lengths of AD and BC are equal. What is the value of r ?

(1) q = 60
(2) p = 90


DS21217


Show Spoiler
Attachment:
1.png


Draw a perpendicular line from C to AB
Now by rule: when two sides are parallel ( AB and CD) and other two sides have equal length ( AD and BC), they inscribe equal angle ( q = q'( angle DAB))

statement 1:
q =60
therefore, q' = 60
by the perpendicular line from D to AB at D',
we know Angle ADD' = 180 - (q' + angle ADD'))
and
angle r = angle ADD'+90
sufficient

statement 2
p =90
this gives information only about triangle ACB
insufficient

option A
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   31 May 2020, 04:48
It’s simpler, correct me if I’m wrong:

Use the opposite angle sum property of trapezoid:
angle D + angle B = 180
Hence Statement 1 is sufficient.

Statement 2 only talks about a particular angle in a triangle. Hence insufficient

Hope this helps!

Posted from my mobile device
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   31 May 2020, 05:05
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Bunuel wrote:

In the figure above, AB ǁ CD, AD is not parallel to BC, and the lengths of AD and BC are equal. What is the value of r ?

(1) q = 60
(2) p = 90


DS21217


Show Spoiler
Attachment:
1.png


It's a trapezium with equal legs hence it may be called an

Isosceles Trapezium



In isosceles Trapezium, Angle DAB = Angle ABC
i.e. Angle r + angle q = 180º

Question: r = ?

Statement 1: q = 60

SUFFICIENT

Statement 2: p = 90

i.e. neither q nor r may be calculated using this information hence

NOT SUFFICIENT

Answer: Option A
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   06 Nov 2020, 17:03
GMATinsight wrote:
Bunuel wrote:

In the figure above, AB ǁ CD, AD is not parallel to BC, and the lengths of AD and BC are equal. What is the value of r ?

(1) q = 60
(2) p = 90


DS21217


Show Spoiler
Attachment:
1.png


It's a trapezium with equal legs hence it may be called an

Isosceles Trapezium



In isosceles Trapezium, Angle DAB = Angle ABC
i.e. Angle r + angle q = 180º

Question: r = ?

Statement 1: q = 60

SUFFICIENT

Statement 2: p = 90

i.e. neither q nor r may be calculated using this information hence

NOT SUFFICIENT

Answer: Option A


Hi GMATinsight,
How is Angle DAB = r ?
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   06 Nov 2020, 18:33
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Quote:
In the figure above, AB ǁ CD, AD is not parallel to BC, and the lengths of AD and BC are equal. What is the value of r ?

Step 1: Understanding the question
When non parallel sides of a trapezium are equal, it is known as an isosceles trapezium.
Few properties of an isosceles trapezium are:
1. base angles are same ie. angle DAB = angle ABC
2. Opposite angles are supplementary ie r + q = 180 and angle DAB + angle BCD = 180
3. Diagonals are equal

Step 2: Understanding statement 1 alone
(1) q = 60
As q + r = 180
r = 120
Sufficient

Step 3: Understanding statement 3 alone
(2) p = 90
As q and r cannot be determined, statement is not sufficient

A is correct
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   06 Nov 2020, 20:42
Expert Reply
SiffyB wrote:
GMATinsight wrote:
Bunuel wrote:

In the figure above, AB ǁ CD, AD is not parallel to BC, and the lengths of AD and BC are equal. What is the value of r ?

(1) q = 60
(2) p = 90


DS21217


Show Spoiler
Attachment:
1.png


It's a trapezium with equal legs hence it may be called an

Isosceles Trapezium



In isosceles Trapezium, Angle DAB = Angle ABC
i.e. Angle r + angle q = 180º

Question: r = ?

Statement 1: q = 60

SUFFICIENT

Statement 2: p = 90

i.e. neither q nor r may be calculated using this information hence

NOT SUFFICIENT

Answer: Option A


Hi GMATinsight,
How is Angle DAB = r ?


SiffyB

I didn't mention that Angle DAB = r anywhere.

angle DAB = angle ABC is only because the given trapezium is an isosceles trapezium
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Re: In the figure above, AB ǁ CD, AD is not parallel to BC, and the length [#permalink] New post   27 Nov 2020, 13:56
Since AD and BC are equal, we have an isosceles trapezoid. Therefore angle DAB and angle q are equal. As well, q + r = 180. To determine the value of r, we need to determine either angle DAB or angle q.

(1) \(q = 60\)

Therefore \(r + q = 180\)
\(r + 60 = 180\); \(r = 120\). SUFFICIENT.

(2) \(p = 90\). We can't determine angle ACD. Therefore we can't determine r. INSUFFICIENT.

Answer is A.
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Re: In the figure above, AB CD, AD is not parallel to BC, and the length [#permalink] New post   09 Feb 2023, 02:03
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