Question

if ∠x is an obtuse angle, then which of the following inequalities is true? it is less than 90 degrees. it is exactly 90 degrees it is any number of degrees between 0 and 360. it is more than 90 degrees and less than 180 degrees. it is any amount more than 90 degrees

Explanation:

Step1: Recall the definition of an obtuse angle

An obtuse angle is defined as an angle that measures more than \(90^{\circ}\) and less than \(180^{\circ}\).

Step2: Analyze each option

• Option1: "It is less than \(90\) degrees" describes an acute angle, not an obtuse angle.
• Option2: "It is exactly \(90\) degrees" describes a right - angle, not an obtuse angle.
• Option3: "It is any number of degrees between \(0\) and \(360\)" is too broad.
• Option4: "It is more than \(90\) degrees and less than \(180\) degrees" matches the definition of an obtuse angle.
• Option5: "It is any amount more than \(90\) degrees" is too broad as angles more than \(180^{\circ}\) (reflex angles) are not obtuse.

Answer:

It is more than \(90\) degrees and less than \(180\) degrees.