Question

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

Answer 1

x = 20°

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)