Question

In the figure ABCD is a parallelogram the m e d g b and DFC are straight lines the measure of angle ADG _ angle MDF is

Answer 1

Answer:

∠ADG - ∠MDF = 14°

Step-by-step explanation:

in Parallelogram opposite angles are equal

and sum of adjacent angle = 180°

=> ∠ABC + ∠BCF = 180°

=> ∠ABD + ∠DBC + 52° = 180°

=> ∠ABD + 90° = 128°

=> ∠ABD = 38°

∠DAB = ∠DAF + ∠FAB

=> ∠DAB = 56° + 52°

=> ∠DAB = 108°

in ΔABD

∠ADB + ∠DAB + ∠ABD = 180°

=> ∠ADB + 108° + 38° = 180°

=> ∠ADB = 34°

∠ADG = ∠ADB = 34°

∠CED = 180° - ∠BED

=> ∠CED = 180° - 72°

=> ∠CED = 108°

in ΔCDE

=> ∠CED + ∠ECD + ∠EDC = 180°

=> 108° + 52° + ∠EDC = 180°

=> ∠EDC = 20°

∠MDF = ∠EDC = 20°

∠ADG - ∠MDF = 34° - 20°

=> ∠ADG - ∠MDF = 14°