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Question
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
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Solution
ABC is a right angled triangle in which
∠A = 90°
and AB = AC
In △ABC,
AB = AC
⇒ ∠C = ∠B …(I) ...[Angles opposite to equal sides]
Now, in △ABC,
∠A + ∠B + ∠C = 180° ...[Angle Sum Property of a △)
⇒ 90° + ∠B + ∠B = 180° ...[∵ ∠A = 90° (Given) and ∠B = ∠C from (I)]
⇒ 2∠B = 180° – 90°
⇒ 2∠B = 90°
⇒ ∠B = 45°
Also, ∠C = ∠B
⇒ ∠C = 45°
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