Question

please solve it...i will the answers good​

Answer 1

Answer:

∠A = 96°

Step-by-step explanation:

let say ∠B = β

∠C = γ

Bisector of  ∠B = β/2

Bisector of ∠C = γ/2

Let say bisector of ∠B & ∠C   BD & CE intersect at O

∠ODE = ∠BDE = 24°

∠OED = ∠CED = 18°

in ΔODE

∠ODE + ∠OED  + ∠EOD = 180°

=> 24° + 18° + ∠EOD = 180°

=> ∠EOD = 138°

∠BOC = ∠EOD = 138°  ( opposite angles)

in Δ BOC

∠OBC + ∠OCB + ∠BOC = 180°

∠OBC = ∠ODB = ∠B/2 = β/2

∠OCB = ∠ECB = ∠C/2 = γ/2

=>  β/2 + γ/2 + 138° = 180°

=> β/2 + γ/2 = 42°

=> β + γ = 84°

in ΔABC

∠A + ∠B + ∠C = 180°

=> ∠A + β + γ = 180°

=>  ∠A + 84° = 180°

=> ∠A = 96°