Question

ABC is a right angle triangle in which angle A is equal to 90 degree and AB is equal to AC find Angle B and angle C

Answer 1

as AB = AC given means angle A = angle C
so,
angle A + angle B + angleC =180
90 +x+x=180
90+2x=180
2x=180-90
2x=90
x=45

Answer 2

ABC is a right angled triangle (given)

Here ∠A = 90°                          (given)

And AB = AC                            (given)

So,

ΔABC is an right isosceles triangle in which ∠A = 90° and AB = BC

So, ∠B = ∠C       [∵ AB = BC]

To be found :

∠B and ∠C

Now,

We know that,

Sum of all interior angles of a triangle is 180°

So,

In triangle ABC,

∠A + ∠B + ∠C = 180°

⇒ 90° + ∠B + ∠B = 180°   [As ∠B = ∠C, we can write ∠B in place of ∠C ]

⇒ 90° + 2 ∠B = 180°

⇒ 2 ∠B = 180° - 90°

⇒ 2 ∠B = 90°

⇒ ∠B = 90° ÷ 2

⇒ ∠B = 45°

Therefore,

∠C = 45°      [ as ∠B = ∠C, and ∠B = 45° ]

Hence,

$\bf \angle{B}\: \:and\: \:\angle{C} \: \:are \: \:45^o \: \:each$