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If the angles A, B and C of $Δ A B C$ satisfy the relation B – A = C – B, then the measure of $∠ B$ is ____ °.

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Detailed Solution

If the angles A, B and C of

Δ A B C

satisfy the relation B – A = C – B, then the measure of

∠ B

is 60°.
Given a triangle which satisfies the relation B – A = C – B.
Neha walks along a path in the shape of an equilateral triangle ABC. Each side of the path is 50 m long. She starts from A and reaches point C via point

Neha walks along a path in the shape of an equilateral triangle ABC. Each side of the path is 50 m long. She starts from A and reaches point C via point

Simplifying,

∠ B − ∠ A = ∠ C − ∠ B ⇒ ∠ B + ∠ B = ∠ C + ∠ A ⇒ 2 ∠ B = ∠ C + ∠ A … … (1)

Using angle sum property,

∠ A + ∠ B + ∠ C = 180 ° ⇒ ∠ B = 180 ° − ∠ A − ∠ C ⇒ ∠ B = 180 ° − (∠ A + ∠ C) … … (2)

From equation 1 and 2,

∠ B = 180 ° − 2 ∠ B ⇒ ∠ B + 2 ∠ B = 180 ° ⇒ 3 ∠ B = 180 ° ⇒ ∠ B = 180 ° 3 ∠ B = 60 °

Hence, the measure of

∠ B

60 ∘

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