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

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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 = \(\frac{180}{3}\)

= 60°(i)

Now, Extend side BC to D,

CA to E and AB to F

Here,

BCD is a straight line segment

∠BCD = Straight line segment = 180°

∠BCA + ∠ACD = 180°

60° + ∠ACD = 180°(From i)

∠ACD = 120°

Similarly,

we can find ∠EAB and ∠FBC also as 120° because ABC is an equilateral triangle.

Therefore,

∠ACD = ∠EAB = ∠FBC = 120°

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

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