I need help trying to get the value of the x angle, here's an image of it

Answer:x = 20°Step-by-step explanation:See the attached diagram. Given that B and C are the two centers of two equal circles. Now, ∠ ECD = 80° also given. Now, Δ BCE is an isosceles triangle as BC = CE = Radius of the circle. So, ∠ EBC = ∠ CEB. Now, ∠ ECD = ∠ EBC + ∠ CEB = 80° ⇒ 2 ∠ EBC = 80° ⇒ ∠ EBC = 40° Again, the triangle Δ ABF is an isosceles triangle as AB = BF = Radius So, ∠ BAF = ∠ BFA = x° Now, ∠ EBC = ∠ BAF + ∠ BFA = 40° ⇒ x° + x° = 40° ⇒ 2x = 40 ⇒ x = 20° (Answer)