In the diagram, square ABCD has sides of length 4, and triangle ABE is equilateral. Line segments BE and AC intersect at P. Point Q is on BC so that PQ is perpendicular to BC and PQ=x.
Determine the measure of angle BPC.
Let's look at triangle BPC
Angle C is 45 degrees (bisected by the diagonal)
Angle ABE is 60 degrees due to equilateral triangle so angle B = 30 degrees
180 -30 - 45 = angle BPC = 105 degrees