The measures of two consecutive angles of a parallelogram are in the ratio 5:4. What is the measure of an obtuse angle of the parallelogram?

##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##.