DEF is a pedal triangle of an equilateral triangle ABC. Let us write the measure of ∠FDA

Given: Pedal triangle is a triangle formed by joining the mid-point of a triangle’s sides.

As we know, in an equilateral triangle, triangles formed after joining the mid points is also an equilateral triangle.

Also, the triangle formed joining the vertx and one of the vertex is also an equilateral triangle.

As we know, the measure of an angle in an equilateral triangle is 60° .

Hence, in Δ DEF

∠FDE = 60°

And, in Δ ADE

∠ADE = 60°

So,

∠FDA = ∠FDE + ∠ADE = 60°

⇒ ∠FDA = 60° + 60°

⇒ ∠FDA = 120°