Question

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What is the measure of angle A B D if the measure of arc B D is 130°?


A. 130

B. 100

C. 75

D. 65

Answer 1

m<ABD==65°

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°