Question:
Find the measure of each exterior angle of an equilateral triangle.
Solution:
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°