In the diagram, if m∠ADB = 26° then find the magnitude of angle AOB and angle ACB.
The measure of the central angle is double the measure of the inscribed angle intercepting the same arc
\begin{equation*}
\begin{split}
\text{m}\angle \text{AOB} & = 2\times \text{m}\angle \text{ADB}\\\\
\text{m}\angle \text{AOB} & = 2\times 26^{\circ}\\\\
\text{m}\angle \text{AOB} & = 52^{\circ}\\\\\\
\end{split}
\end{equation*}
Two or more inscribed angles intercepting the same arc are equal
\begin{equation*}
\begin{split}
\text{m}\angle \text{ACB} & = \text{m}\angle \text{ADB}\\\\
\text{m}\angle \text{ACB} & = 26^{\circ}
\end{split}
\end{equation*}