Answer:
m<ABD==65°
Step-by-step explanation:
we know that
1) The triangle DFB is an isosceles triangle, because
DF=BF=radius of the circle
2) BF is perpendicular to the tangent AC at point B
3) The measure of angle m<ABF=90°
4) The measure of angle m<DFB is equal to the measure of arc BD by central angle
so
m<DFB=130°
5) The measure of angle m<DBF=(180°-m<DFB)/2
so
m<DBF=(180°-130°)/2=25°
6) m<DBF+m<ABD=m<ABF
m<DBF+m<ABD=90°------> complementary angles
25°+m<ABD=90°
m<ABD=90°-25°=65°
