Question

Answer options to both feel in the blanks are 19.5 and 29 and 58

Answer 1

Angles BDC, BAC and BOC are subtended by the same arc (arc BD)

Angles BDC anf BAC are inscribed angles; the inscribed angles subtented by the same arc are equal:

`\begin{gathered} \measuredangle BDC=\measuredangle BAC \\ \\ \measuredangle BAC=29º \end{gathered}`

Angle BDC is an iscribed angle; angle BOC is a central angle; an inscribed angle is half of a central angle that subtends the same arc:

`\begin{gathered} \measuredangle BDC=(1)/(2)\measuredangle BOC \\ \\ \measuredangle BOC=2*\measuredangle BDC \\ \\ \measuredangle BOC=2*29º \\ \\ \measuredangle BOC=58º \end{gathered}`

Then, angle BAC is 29º and angle BOC is 58º