Question

Suppose ABCD is a parallelogram in which angle A = 108'. Calculate angles B, C and D.

Answer 1

If ABCD is a parallelogram
In parallelogram ABCD
m/_A=108·
m/_C=m/_A=108·                                           (opposite angle of a parallelogram are                                                                                       congruent)
m/_A+m/_B=180                                            (adjacent angle of a parallelogram are                                                                                       congruent)
108+m/_B=180
m/_B=180-108
m/_B=72
m/_B=m/_D=72                                              (opposite angle of a parallelogram are                                                                                       congruent)

Answer 2

Consider a,b,c,d to be the vertices of the parallelogram taken in cyclic order.
A = 108 degree
opposite sides are equal 
C = 108 degree
base angles are supplementary 
A+B = 180
B =180-108=72
B and D are opposite . Hence D = 72 degree