+20 In rectangle EFGH, EH = 3 and EF = 4. Let M be the midpoint of \(\overline{EF}\), and let be a X point such that MH = MX and \(\angle MHX = 72^\circ\), as shown below. Find angle XGH, in degrees.
+128448 The key to this problem may not be obvious, at first
With M as a center, construct a circle with radius, MH
Note that MH = MG = MX
So.....this circle will pass through H, X and G
Since MH = MX, then in triangle MHX, angle MHX = angle MXH = 72
So angle HMX = 180 - 72 - 72 = 36
So angle HMX is a central angle in the circle
And angle HGX is an inscribed angle which intercepts the same arc as angle HMX
So....it has (1/2) the measure of angle HMX = (1/2) (36) = 18°
