+130474 See the following
Let D=(0,0) C = (4,0) B (4,3) A = (0,3) and M = (2,3)
AM = 2
AD = 3
And triangle AMD is right with hypotenuse MD
By Pythagoras MD = sqrt [ AM^2 + AD^2 ] = sqrt [ 2^2 + 3^2] = sqrt [13] = MX = MC
Since MDX = 77° and MD = MX , then angle MXD also = 77°
And in triangle MDX, angle DMX = 180 - 77 - 77 = 26°
Construct a circle at M with a radius = MD = MX = MC
Angle DMX is a central angle in the circle intercepting the minor arc DX
But angle XCD is an inscribed angle in the same circle and intercepts the same minor arc
So, angle XCD = (1/2)measure of central angle DMX = (1/2) (26°) = 13°
