1. In circle p line ab is drawn through p lines AC and PC are drawn as well with A, B, and C falling on the circumference of circle P if the measure of arc BC is 60 degrees what is the measure of angle BAC

Answer 1

It is a triangle, so it has to add up to 180 degrees, so use the other numbers to find the measure of BAC.
So
BC is 60 degrees, I'm assuming that the arc would add up to 180 degrees
Then
The measure of the angles could be many different things, but the most obvious is a equilateral triangle, so all of the angles/arcs would be 60 degrees.

Answer 2

Inscribed angles are 1/2 of the central angle subtending the same arc.
So, angle BAC = 30°