Question

Find the value of b.

Answer 1

Answer:
`230^{\circ`

Explanation:

For convenience, I labeled some points as shown in the attached picture.

Also, I assume
`\overline{AB}` and
`\overline{BC}` are tangents to the circle.

1. 
   `\overline{BO} \cong \overline{BO}` (reflexive property)
2. 
   `\overline{AB} \cong \overline{BC}` (tangents drawn from a common external point are congruent)
3. 
   `\angle BAO \cong \angle BCO` (right angles are congruent)

Therefore, we know
`\triangle ABO \cong \triangle CBO` by HL.

Thus, by CPCTC,

`\angle AOB \cong \angle BOC \implies m\angle BOC=65^(\circ)\\\\\implies m\angle AOC=130^(\circ)`

This means the measure of minor arc AC is
`130^(\circ)`, and thus
`b=360^(\circ)-130^(\circ)=\boxed{230^(\circ)}`