##100##

An important property of parallelograms is that consecutive angles are supplementary or that the sum of their measures is ##180##.

If we know that two consecutive angles are in a ##5:4## ratio we can call one of the angles ##5x## and the other ##4x##.

Thus since their sum is ##180##

##4x+5x=180##

##9x=180##

##x=20##

Since the angles are ##5x## and ##4x## plug in ##20## to see that their angle measures are ##100## and ##80##.

Of the two the obtuse angle is ##100##.