Question

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

 

Answer 1

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°` 

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° 

⇒ 60°+∠ACD=180°                [from (1)] 

⇒∠ 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°