# Find the Measure of Each Exterior Angle of an Equilateral Triangle. - Mathematics

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^@ .......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^@

Concept: Properties of a Triangle
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 12 Congruent Triangles
Exercise 12.1 | Q 8 | Page 15

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