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

Question

https://gmatclub.com/forum/download/file.php?id=54723 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 Are You Up For the Challenge: 700 Level Questions 1.png

SiffyB · Accepted Answer

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)

BALAGURU · Answer

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

tapovrat · Answer

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

GMATinsight · Answer

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

SiffyB · Answer

Hi  GMATinsight , 
How is Angle DAB = r ?

QuantMadeEasy · Answer

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

GMATinsight · Answer

SiffyB

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

angle DAB = angle ABC is only because the given trapezium is an isosceles trapezium

Basshead · Answer

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

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

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