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˚##.