Angle sum theorem. find z, x,y and w

x = 65°

y = 49°

z = 114°

w = 93°

Step-by-step explanation:

Since ∠y + 131° = 180°

So ∠y = 180° - 131°

          = 49°

From ΔDEF,

∠x + 42° + 73° = 180°

∠x + 115° = 180°

∠x = 180 - 115

    = 65°

From ΔDGL

∠x + ∠y + ∠DLG = 180°

65° + 49° + ∠DLG = 180°

∠DLG = 180 - 114

          = 66°

Now ∠z + ∠DLG = 180° [Supplementary angles]

∠z = 180 - 66

   = 114°

From ΔIJC,

∠142° + ∠IJC = 180° [ Supplementary angles]

∠IJC = 180 - 142

        = 38°

w + 38° + 49°=180°

w + 87° = 180°

w = 180° - 87°

w = 93°