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)
