Question

show that each angle in an equilateral triangle is equal to 60° each

Answer 1

Given :

• AB=BC=AC

To Prove :

• ∠A=∠B=∠C

Solution :

Let an equilateral triangle be ABC.

Now :

$\longmapsto\tt{AB=BC}$

$\longmapsto\tt{\angle{A}=\angle{C}(Angles\:opp.\:to\:equal\:sides---(1)}$

$\longmapsto\tt{BC=AC}$

$\longmapsto\tt{\angle{A}=\angle{B}---(2)}$

By Equation 1 and 2 :

$\longmapsto\tt{\angle{A}+\angle{B}+\angle{C}=180\degree(Angle\:Sum\:Property}$

$\longmapsto\tt{\angle{A}+\angle{A}+\angle{A}=180\degree}$

$\longmapsto\tt{3\angle{A}=180\degree}$

$\longmapsto\tt{\angle{A}=\cancel\dfrac{180}{3}}$

$\longmapsto\tt\bold{\angle{A}=60\degree}$

Therefore :

$\longmapsto\tt\bold{\angle{A}=60\degree}$

$\longmapsto\tt\bold{\angle{B}=60\degree}$

$\longmapsto\tt\bold{\angle{C}=60\degree}$