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`

Step-by-step explanation:

We know that,

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

On substitution we get,

`\begin{gathered} \angle DPC=(58+110)/(2) \\ =(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)`