ABC is a right angled triangle in which ∠A=90° and AB=AC. Find ∠B and ∠C.
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Given : ABC is a right angled triangle in which ∠A = 90° and AB = AC.
Δ ABC is an isosceles triangle since AB = AC
Therefore, Δ ABC is a right-angled isosceles triangle.
∠ C = ∠ B ……… (1)
[Angles opposite to equal sides are equal]
We know, that sum of angles in a triangle is 180°.
∠ A + ∠ B + ∠ C = 180°
∠ A + ∠ B + ∠ B = 180°
[From eq (1)]
90° + 2∠B = 180°
[∠A = 90°]
2∠B = 180° – 90°
2∠B = 90°
∠B = 90°/2
∠B = 45°
Hence, ∠ B = ∠ C = 45°.
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