Points A,B,Q,D, and C lie on the circle shown and the measures of arcs BQ and QD are 42∘ and 38∘ respectively. The sum of the measures of angles P and Q is<spanclass=′latex−bold′>(A)</span>80∘<spanclass=′latex−bold′>(B)</span>62∘<spanclass=′latex−bold′>(C)</span>40∘<spanclass=′latex−bold′>(D)</span>46∘<spanclass=′latex−bold′>(E)</span>None of these[asy]
size(3inch);
draw(Circle((1,0),1));
pair A, B, C, D, P, Q;
P = (-2,0);
B=(sqrt(2)/2+1,sqrt(2)/2);
D=(sqrt(2)/2+1,-sqrt(2)/2);
Q = (2,0);
A = intersectionpoints(Circle((1,0),1),B--P)[1];
C = intersectionpoints(Circle((1,0),1),D--P)[0];
draw(B--P--D);
draw(A--Q--C);
label("A",A,NW);
label("B",B,NE);
label("C",C,SW);
label("D",D,SE);
label("P",P,W);
label("Q",Q,E);
//Credit to chezbgone2 for the diagram[/asy]