Given: ∆ABC is equilateral triangle.

To prove: ∠CAD = ∠CBE = ∠BCL

Proof:

Let our triangle be ∆ABC, which is equilateral triangle as shown in the figure.

Hence all angles are equal and measure 60° each.

∴ ∠CAB = ∠CBA = ∠BCA = 60° …(1)

Also here, ∠CAD and ∠CBE are exterior angles of the triangle.

So, we know that,

∠CAB +∠CAD = 180° … exterior angle theorem

∠CBA + ∠CBE = 180° … exterior angle theorem

∠BCA + ∠BCL = 180° … exterior angle theorem

From (1) and above statements, we state that,

60° +∠CAD = 180°

60° + ∠CBE = 180°

60° + ∠BCL = 180°

Simplifying above statements,

∠CAD = 180° - 60° = 120°

∠CBE = 180° - 60° = 120°

∠BCL = 180° - 60° = 120°

Hence, the measure of each exterior angle of an equilateral triangle is 120°