Question

in ∆ABC the bisectors of B and C intersect at l.if angle A =90° find angle BIC

Answer 1

Answer:

135 degree

Step-by-step explanation:

Given In ∆ABC the bisectors of B and C intersect at l.if angle A =90° find angle BIC

 Using angle sum property we have

  Angle A + B + C = 180 degree , but angle A = 90

             90 + B + C = 180

                   B + C = 180 - 90 = 90

We have BIC + ICB + IBC = 180

              BIC + 1/2 x C + 1/2 x B = 180

              BIC + 1/2(C + B) = 180

             BIC + 1/2 x 90 = 180

                  BIC + 45 = 180

                BIC = 180 - 45 = 135

                Angle BIC = 135 degree

             

Answer 2

Answer:

Step-by-step explanation:

In Δ BLC we have ,

∠1 + ∠2 + ∠BLC = 180°........(1)

In ΔABC ,

∠A + ∠B + ∠C = 180°

∠A+ 2(∠1) + 2(∠2) = 180°

∠A/2 + ∠1 + ∠2 = 90°

∠1 + ∠2 = 90°- ∠A /2..............(2)

Substituting the value of equation (1)& (2)

90° - ∠A/2 + ∠BLC = 180°

∠BLC = 180 - 90 °+ ∠A/2

∠BLC = 90 ° + ∠A/2

∠BLC = 90° + 90°/2

∠BLC = 90° + 45°

∠BLC = 135°