Question

Show that the angles of
equila teral triangle
an
are 60 each​

Answer 1

Answer:

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Step-by-step explanation:

In a ∆ABC,

AB=BC=CA

therefore, Angle ABC= Angle BCA = Angle CAB =x (Angles opposite to equal sides of a ∆ are equal)

therefore, x+x+x=180° (Sum of angles of a ∆)

= 3x=180°

x=60°

Hence, Proved.

Answer 2

Given :

• AB = BC = AC

To Prove :

• ∠A = ∠B = ∠C = 60°

Solution :

Let an equilateral triangle ABC.

$\longmapsto\tt{AB=AC}$

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

$\longmapsto\tt{BC=AC}$

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

By Equation 1 and 2 :

$\longmapsto\tt{\angle{A}=\angle{B}=\angle{C}}$

$\longmapsto\tt{\angle{A}=\angle{B}=\angle{C}=180\degree\:(A.S.P)}$

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

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

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

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

Therefore :

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

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

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

HENCE PROVED