Question

In ∆DEF, ∠F = 48°, ∠E = 68° and bisector of ∠D meets FE at G. Find ∠FGD

Answer 1

Given ∠F = 48°

∠E = 68°

In ∆DEF,

∠D + ∠F + ∠E = 180°  ...[By angle sum property]

∠D + 68° + 68° = 180°

∠D + 116° = 180°

∠D = 180° – 116°

= 64°

Since DG is the angular bisector of ∠D

∠FDG = ∠GDE

Also ∠FDG + ∠GDE = ∠D

2 ∠FDG = 64°

2 ∠FDG = 64°

∠FDG = `(64^circ)/2` = 32°

∠FDG = 32°

In ∆FDG,

∠FDG + ∠GFD = 180°  ...[By angle sum property of triangles]

32° + ∠FDG + 48° = 180°

∠FDG + 80° = 180°

∠FDG = 180° – 80°

∠FDG = 100°