Suppose on a circle that ∠ABD is formed by a tangent and a secant intersecting outside of the circle creating the minor arcs AC = 68° and CD = 124°.

1. Draw the described circle.
2. What is the measure of ∠ABD?

The answer is:

∠

B

=

sin

−

1

(

20

⋅

sin

(

30

∘

)

15

)

You have to use the law of sines, just as you thought. This law is:

a

sin

∠

A

=

b

sin

∠

B

=

c

sin

∠

C

We only need the first equation here, let's fill in the numbers.

15

sin

(

30

∘

)

=

20

sin

∠

B

We use cross-multiplication, then we find:

sin

∠

B

=

20

⋅

sin

(

30

∘

)

15

then by taking the inverse sine, we find

∠

B

=

sin

−

1

(

20

⋅

sin

(

30

∘

)

15

)

Step-by-step explanation:

Hope it is helpful....