From CIRCLE THEOREM: The angle at the centre of a circle is twice the angle at its circumference.
The above circle with O as its centre subtends an arc BD
The angle at the circumference is 47.7degrees;
[tex]\begin{gathered} \angle Arc\text{ BD=2}\times47.7^o \\ \angle Arc\text{ BD=9}5.4^o \end{gathered}[/tex]The measure of Arc BD is 95.4degrees