PLEASE ANSWER THIS..........

from the given info we get that

AD/CD=DB/DA

In triangles

ADB and CDA,

AD/CD=DB/DA

angle ADB=angleCDA=90 each  (given)

so

triangle ADB similar to triangle CDA (SAS rule)

so

DAB=DCA..corr angles of sim triangles are equal   ...(i)

but

DAB+DBA=90 (as AD perpendicu.to BC)

so

DCA+DBA=90 from(i)

So in triangle ABC,

Angle C+angle B=90

So

angle A=90 (Angle.Sum Prop.)