Question

Find each measure. When point 0 is shown, it is the center of the circle

Answer 1

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

`\begin{gathered} \hat{mABC}=360-130\degree \\ mABC=230\degree \end{gathered}`

The angle at B is given as:

`\begin{gathered} m\angle ABC=(1)/(2)* mABC(Angle\text{ }subtended\text{ }at\text{ }the\text{ }center\text{ }is\text{ }twice\text{ }that\text{ }at\text{ }circumference) \\ m\angle ABC=(1)/(2)*130 \\ m\angle ABC=65\degree \end{gathered}`

Final answer:

`\begin{gathered} mABC=230\degree \\ m\angle ABC=65\degree \end{gathered}`