Question

please help me solve this problem.

Answer 1

In ∆ABD AB=AD
Hence ∠ABD=∠ADB=42°
Now ∠ADB=∠DAG+∠AGD
Or, ∠ADB=2∠AGD
Or,∠AGD=1/2∠ADB
Or, ∠ADG=42°/2=21°
i.e y=21°
In ∆ OMG OM=OG
therefore ∠OMG=∠OGM=y=21°
Now x=∠AME=∠AMO=∠AMG-∠OMG=∠AMD-∠OMG=90°-21°=69°
Hence x-y=69°-21°=48°