Question

in the figure below, \\( \overline{ab} \\) is a diameter of circle \\( p \\). what is the arc measure of minor arc \\( \overarc{ac} \\) in degrees?

Explanation:

Step1: Recall diameter property

A diameter divides a circle into a semicircle, so the central angle for arc \( AB \) is \( 180^\circ \).

Step2: Find angle \( \angle APC \)

We know \( \angle BPC = 69^\circ \). Since \( \angle APB = 180^\circ \) (diameter), then \( \angle APC = 180^\circ - 69^\circ \).
\( \angle APC = 111^\circ \)

Step3: Arc measure equals central angle

The measure of a minor arc is equal to the measure of its central angle. So arc \( AC \) has measure equal to \( \angle APC \), which is \( 111^\circ \).

Answer:

\( 111 \)