Question

n the circle below, if arc AC = 54 °, and arc BD = 158 °, find the measure of < BPD.

Answer 1

The relation between the arcs AC and BD with the angle BPD is given by:

$\begin{gathered} \angle BPD=\frac{arc\text{ AC}+arcBD}{2} \\ \angle BPD=\frac{54\degree+158\degree}{2} \\ \angle BPD=\frac{212\degree}{2} \\ \angle BPD=106\degree \end{gathered}$