Question

∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 78° and minor arc CD = 124°, what is the measure of ∠ABD? A) 23° B) 39° C) 40° Eliminate D) 46°+-

Answer 1

Minor arc AD is 360° -124° -78° = 158°. Then angle ABD is
  (158° -78°)/2 = 40°

The appropriate selection is
  C) 40°

Answer 2

Answer:

40°

Step-by-step explanation:

First, find minor arc AD.

minor arc AD = 360 - 78 - 124 = 158

then,

∠ABD =

1

2

(minor arc AD - minor arc AC)

∠ABD =

1

2

(158 - 78)

∠ABD =

1

2

80

∠ABD = 40°