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705-805 (Hard)|   Geometry|      
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 13 Aug 2010, 10:49
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

50% (02:41) correct 50% (02:49) wrong based on 115 sessions

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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


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D
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Bull78
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 13 Aug 2010, 11:44
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I got C

Could you please provide OA.

Thanks
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rxs0005
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 13 Aug 2010, 13:51
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The OA is D without explanation i think its a TYPO

can you let us know how you got C
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 13 Aug 2010, 14:21
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rxs0005
The OA is D without explanation i think its a TYPO

can you let us know how you got C
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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: \(\angle{BCD}-\angle{ADE}=?\).

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.
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 13 Aug 2010, 16:35
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good Qn.
Thanks Bunuel.
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 13 Aug 2010, 16:40
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thanks i now get it

i was taking interior angles as 180 which is not necessarily true
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 10 May 2018, 09:29
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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.
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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d 07 Apr 2021, 02:27
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