It is known that BP=PQ=QC=AP=AQ, so AP=AQ=PQ, so in the triangle APQ, the three sides are equal, so the triangle APQ is a regular triangle, so the angle PAQ=60 degrees.

There is an angle APQ=60 degrees, so the angle APB is 120 degrees. In triangle ABP, BP=AP, and the triangle is an isosceles triangle, so the angle BAP=30 degrees. Similarly, it can be obtained that CAQ angle =30 degrees.

To sum up, the angle BAC= 120 degrees.