In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d

Question

https://gmatclub.com/forum/download/file.php?id=12342 In the figure above, if angle ABC = 110 degrees, and angle AED = 100 degrees, then angle ADE is how many degrees smaller than angle BCD? (1) Angle DAB = 45 degrees (2) Angle ADC + angle BCD = 205 degrees DS.jpg

Bull78 · Answer

I got C

Could you please provide OA.

Thanks

rxs0005 · Answer

The OA is D without explanation i think its a TYPO

can you let us know how you got C

Bunuel · Answer

No typo OA is correct.

Important property of polygons: Sum of Interior Angles of a polygon is  180(n-2)  where  n  is the number of sides.

So for quadrilateral sum of the angles equals to  180(4-2)=360  degrees.

Given:  \angle{ABC}=110  and  \angle{AED}=100 . Question:  \angle{BCD}-\angle{ADE}=? .
 https://gmatclub.com/forum/download/file.php?id=12342 
Now as  \angle{ABC}=110  and  \angle{AED}=100  and the sum of all angles is 360 degrees then the sum of other two angles in quadrilateral must be  \angle{BCD}+\angle{BAE}=360-(110+100)=150 .

(1)  \angle{DAB}=45  -->  \angle{BAE}=\angle{DAB}+\angle{DAE}=45+\angle{DAE} , but  \angle{DAE}=180-100-\angle{ADE}=80-\angle{ADE}  (the sum of interior angles in triangle ADE equals to 180 degrees) -->  \angle{BAE}=45+80-\angle{ADE}=125-\angle{ADE} . So  \angle{BCD}+\angle{BAE}=150  becomes  \angle{BCD}+125-\angle{ADE}=150  -->  \angle{BCD}-\angle{ADE}=25 . Sufficient.

(2)  \angle{BCD}+\angle{ADC}=205  -->  \angle{ADC}=180-\angle{ADE}  (straight line) -->  \angle{BCD}+180-\angle{ADE}=205  -->  \angle{BCD}-\angle{ADE}=25 . Sufficient.

Answer: D.

Hope it's clear.

itsnotover · Answer

good Qn.
Thanks Bunuel.

rxs0005 · Answer

thanks i now get it

i was taking interior angles as 180 which is not necessarily true

GMATBusters · Answer

Hii
Please observe that both statement 1 & 2 gives same results.

(1) Angle DAB = 45 degrees
if in quadrilateral, Angle DAB = 45 (St1), Angle ABC= 110 (Question stem)
then as the sum of Angles in a Quadrilateral is 360,
Angle ADC + angle BCD = 205 degrees= Statement 2.
(you need not calculate this, you can infer that Angle ADC + angle BCD = can be calculated from St 1)

(2) Angle ADC + angle BCD = 205 degrees

Since, both statement 1 & 2 gives same results Answer is D or E.
Eliminate all other choices.

We need to check any one of the statements, Let check using statement1

Now , we can solve this question using construction approach:
Try to construct the Quadrilateral.
See the Sketch.

Attachment:

WhatsApp Image 2018-05-10 at 21.56.11.jpeg [ 67.38 KiB | Viewed 4287 times ]

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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d

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