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Interior Angles of a Quadrilateral

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by nakul_anand » Sun May 02, 2010 5:09 pm
Is the measure of one of the interior angles of the quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of the quadrilateral ABCD are right angles.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD.


[spoiler]OA:E[/spoiler]
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Source: — Data Sufficiency |
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by liferocks » Sun May 02, 2010 5:56 pm
I am getting the ans as C--both together are sufficient

clearly either of the conditions alone is not sufficient.

together , angle CDA =angle DAB =90..hence angle ABC + angle BCD =180
since angle ABC =2*angle BCD ...angle BCD=60

Can someone please explain what is wrong with the approach?
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by this_time_i_will » Sun May 02, 2010 6:11 pm
nakul_anand wrote:Is the measure of one of the interior angles of the quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of the quadrilateral ABCD are right angles.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD.


[spoiler]OA:E[/spoiler]
quite a subtle question.

I: clearly NOT SUFFICIENT.
II: clearly NOT SUFFICIENT.

Both: As shown by liferocks above, one of the angle may be 60 degree or as shown below may not be 60 degree:
Let,
angle ABC = 90.
angle BCD = 45.
angle BAD = 90.
so, ADC = 135.
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by liferocks » Sun May 02, 2010 6:14 pm
this_time_i_will wrote:
nakul_anand wrote:Is the measure of one of the interior angles of the quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of the quadrilateral ABCD are right angles.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD.


[spoiler]OA:E[/spoiler]
quite a subtle question.

I: clearly NOT SUFFICIENT.
II: clearly NOT SUFFICIENT.

Both: As shown by liferocks above, one of the angle may be 60 degree or as shown below may not be 60 degree:
Let,
angle ABC = 90.
angle BCD = 45.
angle BAD = 90.
so, ADC = 135.
Got the point..Thanks!
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