In ΔABC, D is a point on BC. If $$\frac{{{\text{AB}}}}{{{\text{AC}}}} = \frac{{{\text{BD}}}}{{{\text{DC}}}},$$   ∠B = 75° and ∠C = 45°, then ∠BAD is equal to :

Solution (By Examveda Team)

Since $$\frac{{{\text{AB}}}}{{{\text{AC}}}} = \frac{{{\text{BD}}}}{{{\text{DC}}}}$$
Hence AD is an angle Bisector
Hence ∠BAD $$ = \frac{{{{180}^ \circ } - \left( {{{75}^ \circ } + {{45}^ \circ }} \right)}}{2} = \frac{{{{60}^ \circ }}}{2} = {30^ \circ }$$