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Question
Find the measure of each exterior angle of an equilateral triangle.
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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^@` .......1
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^@`
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^@`
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