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°