In rectangle ABCD, we have AD = 3 and AB = 4. Let M be the midpoint of AB, and let X be the point such that MD = MX, angle MDX = 79 degrees, and A and X lie on opposite sides of DM. Find angle XCD, in degrees.

Draw a straight line from point M to point C.

∠CMB = ∠MCD = arctan(3 / 2) = 56.30993247º

∠DMX = 180 - 2 * 79 = 22º

∠CMX = 180 - [(2*∠CMB) + 22] = 45.38013505º

∠MCX = 1/2 (180 - ∠CMX ) = 67.30993247º

∠XCD = ∠MCX - ∠MCD = 11º