Draw BL perpendicular to AC and join L to D. Since ∠BCL=30° we get ∠CBL=60°. since BLC is right tringle with ∠BCL=30°,we have BL=
BC
2
=BD. Thus in triangle BLD, we observe that BL=BD and ∠DBL=60° and ∠ADB=45°, we get ∠ADL=15°. But ∠DAL=15°.Thus LD=LA.we hence have LD=LA=LB. This implies that L is the circumcenter of the triangle BDA. Thus ∠BAD=
1
2
∠BLD=
1
2
×60°=30° 30°+45°+∠ABC=180° Hence ∠ABC=105° so the value of ∠BAD and ∠ABC are 30° and 105° respectively