Question

The ratio of two interior angles of a parallelogram is \(4: 5\). What is the degree measure of one of the two obtuse angles of the parallelogram?

Answer 1

If the ratio of the two angles is \(4: 5\), then the angles are \(4 x\) and \(5 x\). Since the angles of a parallelogram sum to \(360^{\circ}\), we have \(4 x+5 x+4 x+5 x=360\). Therefore, \(18 x=360\), so \(x=20\). One of the obtuse angles is \(5 x\), which is \(100^{\circ}\).

 

Final Answer: The final answer is \(100^{\circ}\).