Data Sufficiency

Only A is sufficient to deduct that X+Y is 210. We don't need individual values for X & Y.

40 + B + C =180

B+C = 140 ==> (B+C)/2 = 70

Let the point of intersection be O.

Angle BOC = 180 ; BOD = 70 ; COE = 70 ; DOE = 110

110 - C/2 = 180 - Y (eq 1)
110- B/2 = 180 - X

i.e 220-70=360-(X+Y)

X+Y = 210.

A Sufficient

[quote="sud21"][url=https://postimage.org/image/qoasoztb9/][img]https://s18.postimage.org/qoasoztb9/07_130.jpg[/img][/url][/quote]

What is the OA?

A seems right.

as we see that BE & CD is bisectors of angle ABC & angle ACB respectively.

so from stat 1), we know that angle BAC = 40
so, angle ABC + angle ACB = 140
so, (angle ABC + angle ACB)/2 = (angle EBC + angle DCB) = 70
so angle BOC = 110 (sum of angles of a triangle is 180)
SO, angle DOE = 110
we know that angle BAC = 40
as the sum of angles of a quadrilateral is 360
so (x+y) = 360 - (angle DOE + angle DAE)
= 210

Anurag@Gurome wrote:

sud21 wrote:

(1) Angle A = 40º
Let the point of intersection of CD and BE be I.
So angle BIC = 90 + (40/2) = 110 = angle DIE.
So, (x + y) = 360 - (110 + 40) = 210; SUFFICIENT.

(2) Angle ABC = Angle ACB implies ABC is an isosceles triangle. But again we are not able to find the values of x and y; NOT sufficient.

The correct answer is A.

Please give the proof that the opposite angle formed by angle bisectors with the third vertex is 90 + half angle of vertex

Please provide proof for the theorems used in solving this question