From the figure, We can notice that Sum of the angles (∠AKC and ∠AKE) should be equal to 180°
Because ∠AKC and ∠AKE make a Linear Pair
⇒ ∠AKC + ∠AKE = 180°
⇒ 5x + 12x + 27 = 180
⇒ 17x = 180 - 27
⇒ 17x = 153
⇒ x = 9°
⇒ ∠AKE = 12(9) + 27 = (108 + 27) = 135°
Answer : ∠AKE = 135°