Question

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?

Answer 1

`100˚`

Explanation:

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˚`.