Question

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

Answer 1

Data : ABC is a right angled triangle in which 

∠A = 90° and AB = AC. 

To Prove: 

∠B = ? and ∠C = ? 

Proof: 

In ∆ABC, AB = AC, then 

∴ ∠B = ∠C. 

In ∆ABC, 

∠A + ∠B + ∠C = 180° 

90 + ∠B + ∠C = 180° 

∠B + ∠C = 180 – 90° 

∠B + ∠C = 90° 

∠B + ∠C = 90°. 

But, ∠B = ∠C,

∠B + ∠C = 90° 

∠B + ∠C = 90° 

2∠B = 90° 

∴ ∠B = \(\frac{90}{2}\) = 45 

∴ ∠C = 45° 

∵∠ABC = ∠ACB