By angle sum property we know that the sum of all the angles of a triangle is 180We 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=18060o3x = 180⇒x = 60Hence the answer.
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Step-by-step explanation:
By angle sum property we know that the sum of all the angles of a triangle is 180We 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=18060o3x = 180⇒x = 60Hence the answer.
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Verified answer
Answer:
Show that the angles of an equilateral triangle are 60° each.
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Show that the angles of an equilateral triangle are 60° each.
Solution:
Let's draw an equilateral triangle ABC as shown below.
Show that the angles of an equilateral triangle are 60° each
Therefore,
AB = BC = AC
∴ ∠C = ∠A = ∠B (Angles opposite to equal sides of a triangle are equal)
Let ∠A = ∠B = ∠C be x.
In △ ABC,
∠A + ∠B + ∠C = 180° (Angle sum property of a triangle)
⇒ x + x + x = 180°
⇒ 3x = 180°
⇒ x = 60°
∴ ∠A = ∠B = ∠C = 60°
Hence, in an equilateral triangle, all interior angles are of measure 60°.