MathDB

A convex quadrilateral

ABCD

with BC\equal{}CD and \angle CBA\plus{}\angle DAB>180^{\circ} is given. Suppose that

W

and

Q

are points on the sides

BC

and

DC

respectively (distinct from the vertices) such that AD\equal{}QD and

WQ \parallel AD.

Also suppose that

AQ

and

BD

intersect at a point

M

that is equidistant from the lines

AD

and

BC

. Prove that angle \angle BWD\equal{}\angle ADW.

Problem Statement