To determine the correct range for the measure of an obtuse angle, we need to understand the definitions of various types of angles.
1. Acute Angle: An acute angle measures less than [tex]\(90^{\circ}\)[/tex].
2. Right Angle: A right angle measures exactly [tex]\(90^{\circ}\)[/tex].
3. Obtuse Angle: An obtuse angle measures more than [tex]\(90^{\circ}\)[/tex] but less than [tex]\(180^{\circ}\)[/tex].
4. Straight Angle: A straight angle measures exactly [tex]\(180^{\circ}\)[/tex].
Given these definitions, we are specifically interested in the obtuse angle.
- Option A states that an obtuse angle's measure is between [tex]\(90^{\circ}\)[/tex] and [tex]\(180^{\circ}\)[/tex].
- Option B states that an obtuse angle's measure is exactly [tex]\(90^{\circ}\)[/tex]. This is actually the measure of a right angle, not an obtuse angle.
- Option C states that an obtuse angle's measure is between [tex]\(0^{\circ}\)[/tex] and [tex]\(90^{\circ}\)[/tex]. This describes an acute angle, not an obtuse angle.
By analyzing the options according to the definitions of the angles:
- Option A correctly identifies the range of an obtuse angle as being between [tex]\(90^{\circ}\)[/tex] and [tex]\(180^{\circ}\)[/tex].
Thus, the measure of an obtuse angle is correctly described by option A:
A. between [tex]\(90^{\circ}\)[/tex] and [tex]\(180^{\circ}\)[/tex].
