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

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.

good Qn.
Thanks Bunuel.

thanks i now get it

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

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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