Question

8.Show that the angles of an equilateral triangle are 60° each.
​

Answer 1

Answer:

AB = BC = CA ( equilateral triangle)

therefore, angle ABC = BAC = ACB

angle (ABC + BAC + ACB ) = 180 ° ( s. of all angles in a triangle )

3ABC = 180°

ABC = 180°/ 3 .......therefore all angles in a triangle is 60°

Answer 2

Let ABC be an equilateral angle as shown above.

Here,$BC=AC=AB$ (Since the length of all side is same)

$\longrightarrow{A=B=C}$ (Sides opposite to the equal angles are equal)

$\underline{\underline{\rm{Also,we\:know\:that,}}}$

$\large\sf{A+B+C = 180°}$

$\large\sf{\longrightarrow{3A=180°}}$

$\large\sf{\longrightarrow{A=\frac{180°}{3}}}$

$\large\sf{\longrightarrow{A=60°}}$

So, A = B = C = 60°

So, the angles of equilateral triangle are always 60°.