Question

show that each angle of an equilateral triangle is 60°​

Answer 1

Answer:

60°+60°+60°=180°

Step-by-step explanation:

because all sides of equilateral triangle are equal. then all angles are also equal.

Answer 2

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• show that each angle of an equilateral triangle is 60°

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Let ∆ABC be an equilateral triangle.

Then,BC = CA = AB

$⇒ BC = CA \: and \: CA = Ab \:$

$⇒ \angle \: A = \angle \: B \: and \: \angle \: B \: = \angle \: C \\ \: \: \: \: \: [\therefore \: angles \: opposite \: to \: equal \: sides \: are \: equal]$

$⇒ \angle \: A = \angle \: B = \angle \: C = x\degree \: \: \: \: (say).$

But, we know that the sum of all angles of a triangle is 180°

$\therefore \: \angle \: A + \angle \: B + \angle \: C = 180\degree$

$⇒ x\degree + x\degree + x\degree = 180\degree$

$⇒ 3x\degree = 180\degree ⇒ x = 60.$

$\therefore \: \angle \: A = \angle \: B = \angle \: C \: = 60\degree$

Hence, each angle of an equilateral triangle is 60°

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