Question

Show that the angles of an equilateral triangle are of measure of 60 degree each

Answer 1

let a be the angle of triangle
since 3 sides are equal
therefore,all angles will be equal
<a+<a+<a=180
3<a=180
<a=180\3
<a=60°

Answer 2

We know that,

Equilateral triangle is a triangle in which all three sides are equal and all three interior angles are equal.

Let,

ABC be an equilateral triangle

So,

AB = AC = BC

$\bf \angle{A}=\angle{B}=\angle{C}$

 

To be proof :

All three interior angles of equilateral triangle are 60°

 

So,

Here,

$\bf \angle{A}+\angle{B}+\angle{C}=180^o$

⇒ $\bf \angle{A}+\angle{A}+\angle{A}=180^o$    

[ ∴ as  $\bf \angle{A}=\angle{B}=\angle{C},\: \:we \: \:can\:  \:write \: \: \angle{B}\: \: and \: \:\angle{C}\: \: as \: \: \angle{A}$ ]

⇒ $\bf 3 \angle{A} =180^o$

⇒ $\bf \angle{A} =\frac{180}{3}$

⇒ $\bf \angle{A}=60^o$

Hence,

$\bf \angle{A}=60^o$ so,

$\bf \angle{A}=\angle{B}=\angle{C}=60^o \: \: each$

Hence proved.