Math Problem Solver

Let $ABCD$ be a square of side length 1. Let $P$ be a point on side $\overline{CD}$ such that $\angle DAP = 20^\circ.$ Let $Q$ be a point on side $\overline{BC}$ such that $\angle BAQ = 25^\circ.$ Find the perimeter of triangle $CPQ.$

[asy]

unitsize(2 cm);

pair A, B, C, D, P, Q;

A = (0,1);

B = (0,0);

C = (1,0);

D = (1,1);

P = extension(A, A + dir(-20), C, D);

Q = extension(A, A + dir(-65), B, C);

draw(A--B--C--D--cycle);

draw(A--P--Q--cycle);

label("$A$", A, NW);

label("$B$", B, SW);

label("$C$", C, SE);

label("$D$", D, NE);

label("$P$", P, E);

label("$Q$", Q, S);

[/asy]