Answer: [tex]230^{\circ[/tex]
Step-by-step explanation:
For convenience, I labeled some points as shown in the attached picture.
Also, I assume [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex] are tangents to the circle.
- [tex]\overline{BO} \cong \overline{BO}[/tex] (reflexive property)
- [tex]\overline{AB} \cong \overline{BC}[/tex] (tangents drawn from a common external point are congruent)
- [tex]\angle BAO \cong \angle BCO[/tex] (right angles are congruent)
Therefore, we know [tex]\triangle ABO \cong \triangle CBO[/tex] by HL.
Thus, by CPCTC,
[tex]\angle AOB \cong \angle BOC \implies m\angle BOC=65^{\circ}\\\\\implies m\angle AOC=130^{\circ}[/tex]
This means the measure of minor arc AC is [tex]130^{\circ}[/tex], and thus [tex]b=360^{\circ}-130^{\circ}=\boxed{230^{\circ}}[/tex]
