Question

36. Show that each angle of equilateral triangle is 60°​

Answer 1

$\huge{\underline{\sf{Question :-}}}}$

Show that each angle of equilateral triangle is 60°

$\huge{\underline{\sf{Answer :-}}}}$

$\boxed{ \sf \red{ Given, }}$

• Let ABC be an equilateral triangle.

$\green{\underline\bold{We\: know\:that,}}$

✏ In an equilateral triangle, all sides are equal.

✏ ∴ AB = BC = AC

$\boxed{ \sf \blue{ To\: Prove,}}$

✏ Each angle of equilateral triangle is 60°

✏ i.e ∠A + ∠B + ∠C = 60°

$\boxed{ \sf \red{ Proof,}}$

⇒ AB = AC

⇒ ∠B = ∠C ──────────── ( i )

( ∵ Angles opposite to opposite sides are equal )

Also,

⇒ AC = AB

⇒ ∠A = ∠B ──────────── ( ii )

( ∵ Angles opposite to opposite sides are equal )

From ( i ) and ( ii ), we get:

⇒ ∠A = ∠B = ∠C ──────────── ( iii )

$\huge \red\{In \:triangle\: ABC,\:}$

⇒ ∠A + ∠B + ∠C = 180° ( Angle sum property of a ▲ )

⇒ ∠A + ∠A + ∠A = 180°

⇒ 3∠A = 180°

⇒ ∠A = 180°/3

⇒ ∠A = 60°

∴ ∠A + ∠B + ∠C = 60°

$\green{\underline\bold{Hence\: proved.}}$

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Answer 2

Answer:

By angle sum property we know that the sum of all the angles of a triangle is 180

We know that all the sides of a triangle are equal.

i.e all the angles of an equilateral triangle are equal.

Let each angle be x.

x+x+x=180

60o

3x = 180

⇒x = 60

Hence the answer.

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