SOLUTION:
Case: Circle theorems
Method:
From the given circle,
The angle subtended by the arc AC at the center of the circle is 130 degrees
Hence
The major arc ABC is
[tex]\begin{gathered} \hat{mABC}=360-130\degree \\ mABC=230\degree \end{gathered}[/tex]The angle at B is given as:
[tex]\begin{gathered} m\angle ABC=\frac{1}{2}\times mABC(Angle\text{ }subtended\text{ }at\text{ }the\text{ }center\text{ }is\text{ }twice\text{ }that\text{ }at\text{ }circumference) \\ m\angle ABC=\frac{1}{2}\times130 \\ m\angle ABC=65\degree \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} mABC=230\degree \\ m\angle ABC=65\degree \end{gathered}[/tex]