Question

If I is the incentre of ΔXYZ, ∠IYZ = 30° and ∠IZY = 40°, find ∠YXZ.

Answer 1

Since I is the incentre of ΔXYZ

∠IYZ = 30° ⇒ ∠IYX = 30°

∠IZY = 40° ⇒ ∠IZX = 40°

∴ ∠XYZ = ∠XYI + ∠IYZ = 30° + 30°

∠XYZ = 60°

lll ly ∠XYZ = ∠XZI + ∠IZY = 40° + 40°

∠XYZ = 80°

By angle sum property of a triangle

∠XZY + ∠XYZ + ∠YXZ = 180°

80° + 60° + ∠YXZ = 180°

140° + ∠YXZ = 180°

∠YXZ = 180° – 140°

∠YXZ = 40°