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In a △ABC, AB = AC and ∠A = 50°, find ∠B and ∠C.

Triangles

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Answer

In a △ABC, AB = AC and ∠A = 50°, find ∠B and ∠C. R.S. Aggarwal Mathematics Solutions ICSE Class 9.

In △ABC,

AB = AC

⇒ ∠B = ∠C = a (let) [Angles opposite to equal sides are equal]

By angle sum property of a triangle,

⇒ ∠A + ∠B + ∠C = 180°

⇒ 50° + a + a = 180°

⇒ 2a = 180° - 50°

⇒ 2a = 130°

⇒ a = 130°2\dfrac{130°}{2}

⇒ a = 65°.

⇒ ∠B = ∠C = 65°

Hence, ∠B = ∠C = 65°.

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