Question

n the circle below, if arc AC = 60 °, and arc BD = 148 °, find the measure of < BPD.

Answer 1

Using the diagram below, the angles of intersecting chords theorem states that

Then,

$\begin{gathered} \Rightarrow\angle1=\frac{1}{2}(\angle arc(AB)+\angle arc(CD)) \\ and \\ \angle2=\frac{1}{2}(\angle arcBC+\angle arcDA) \end{gathered}$

Furthermore, since angles <1 and <3, and <2 and <4 are two pairs of vertical angles,

$\begin{gathered} \angle1\cong\angle3 \\ and \\ \angle2\cong\angle4 \end{gathered}$

Thus, in our case,

$\angle BPD=\frac{1}{2}(\angle arcAC+\angle arcBD)=\frac{1}{2}(60+148)=104$

Therefore, the answer is 104°, option d.