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CBSE Class 9 Mathematics Question 15 of 21

Triangles — Question 7

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Question 7

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Answer

Given :

AB = AC and ∠A = 90°

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C. NCERT Class 9 Mathematics CBSE Solutions.

We know that,

Angles opposite to equal sides are also equal.

∠C = ∠B = x (let)

In Δ ABC,

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

⇒ 90° + ∠B + ∠C = 180°

⇒ 90° + x + x = 180° (From(1))

⇒ 2x = 180° - 90°

⇒ 2x = 90°

⇒ x = 90°2\dfrac{90°}{2}

⇒ x = 45°.

∴ ∠B = ∠C = 45°

Hence, ∠B = 45° and ∠C = 45°.