Find the measure of each exterior angle of an equilateral triangle.

Given to find the measure of each exterior angle of an equilateral triangle consider an equilateral triangle ABC.

We know that for an equilateral triangle

AB = BC = CA and ∠ABC = ∠BCA = CAB =180°/3 = 60° .... (i)

Now,

Extend side BC to D, CA to E and AB to F.

Here BCD is a straight line segment

BCD = Straight angle =180°

∠BCA + ∠ACD = 180° [From (i)]

60° + ∠ACD = 180°

∠ACD = 120°

Similarly, we can find ∠FAB and ∠FBC also as 120° because ABC is an equilateral triangle

∠ACD = ∠EAB - ∠FBC = 120°

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