Question

Determine the measure of each of the equal angles of a right angled isosceles triangle.
OR
ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Answer 1

Answer:

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Answer 2

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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