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I think you forgot to mention that AE and BC are parallel. I am assuming they are parallel.

If AE and BC are parallel, ∠DAE = ∠ABC ⇒ x+19 = y - 11 ⇒ x = y - 11 - 19 ⇒ x = y - 30

∠BAC, ∠ABC and ∠ACB are the three angles of a triangle. Sum of these angles is 180°. (2x+y)°+ (y-11)°+ (x+11)° = 180° ⇒ 2x+y + y - 11 + x + 11 = 180 ⇒ 3x + 2y = 180 ⇒ 3(y-30) + 2y = 180 ⇒ 5y - 90 = 180 ⇒ 5y = 270 ⇒ y = 270/5 = 54° x = y - 30 = 24°

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The sum of angles in triangle ABC = 180 deg => angle BAC + angle ABC + angle ACB = 180° 2x+y + y - 11 + x + 11 = 180° 3x + 2y = 180° --- (1) Angle DAE = angle ABC as AE parallel to BC. DAB is the transversal line. x+19 = y - 11 y - x = 30° --- (2)

(1) + 3 * (2) => 5 y = 270° => y = 54° using (2) we get : x = 24°

Now the angles are ∠DAE = x+19° = 43° ∠BAC = 2x+y = 102° ∠ ABC = y - 11° = 43° ∠ACB = x + 11° = 35°