OPQRSTUVWX is a regular decagon. A rotation of

degrees about U maps X to R. Given

, find

Two lines

and m intersect at O at an angle of

. Let A be a point inside the acute angle formed by

and m. Let B and C be the reflections of A in lines

and m, respectively. Find the number of degrees in

.

Equilateral triangle ABC has centroid G. Triangle A'B'C' is the image of triangle ABC upon a dilation with center G and scale factor -2/3. Let K be the area of the region that is within both triangles. Find K/[ABC].