Question

In the diagram below, if arc AB measures 58 ° and arc DC measures 110 °, find the measure of < BPC.

Answer 1

Given:

$\begin{gathered} m(\hat{AB})=58^{\circ} \\ m(\hat{DC})=110^{\circ} \end{gathered}$

To find: The angle

$\angle BPC$

Explanation:

We know that,

$\angle DPC=\frac{\hat{mAB}+\hat{mDC}}{2}$

On substitution we get,

$\begin{gathered} \angle DPC=\frac{58+110}{2} \\ =\frac{168}{2} \\ \angle DPC=84^{\circ} \end{gathered}$

Using the linear pair,

$\begin{gathered} \angle BPC+\angle DPC=180 \\ \angle BPC+84=180 \\ \angle BPC=180-84 \\ =96^{\circ} \end{gathered}$

Final answer:

The correct option is b.

$\angle BPC=96^{\circ}$