To Find: Measure of each exterior angle of an equilateral triangle

Consider an equilateral triangle ABC.

We know that, for an equilateral triangle

AB = AC =CA

And, ∠ABC = ∠BCA = ∠CAB =

= 60^o (i)

Now, Extend side BC to D,

CA to E and AB to F

Here,

BCD is a straight line segment

∠BCD = Straight line segment = 180^o

∠BCA + ∠ACD = 180^o

60^o + ∠ACD = 180^o (From i)

∠ACD = 120^o

Similarly, we can find ∠EAB and ∠FBC also as 120^o because ABC is an equilateral triangle.

Therefore, ∠ACD = ∠EAB = ∠FBC = 120^o

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