# <span lang="EN-US

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° + 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°

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