Polygon abcde rotates 45° clockwise about point f to produce polygon fghij as shown. what is mbcd?

Polygon FGHIJ is the result of the rotation of ABCDE. 

A = F ⇒ 117°
B = G ⇒ 90°
C = H ⇒ 127°
D = I ⇒ 90°
E = J ⇒ 117°

The measure of angle BCD remains the same because the rotation involves the whole polygon. Thus, it is still 127°