Let's consider the definition and properties of the different types of angles.
1. Acute Angle: An angle that is less than 90 degrees.
2. Right Angle: An angle that is exactly 90 degrees.
3. Obtuse Angle: An angle that is greater than 90 degrees but less than 180 degrees.
4. Straight Angle: An angle that is exactly 180 degrees.
Given that we are asked about [tex]\(\frac{1}{2}\)[/tex] of an obtuse angle:
Obtuse angles are between 90 and 180 degrees. To determine the type of angle that results from taking half of an obtuse angle, let's analyze the possible values.
1. Let's take the lower bound of an obtuse angle, which is slightly greater than 90 degrees. Half of slightly more than 90 degrees is slightly more than 45 degrees.
2. Let's take the upper bound of an obtuse angle, which is slightly less than 180 degrees. Half of slightly less than 180 degrees is slightly less than 90 degrees.
We can see that no matter what specific value between 90 and 180 degrees is chosen, halving an obtuse angle will always result in an angle that is between 45 degrees and 90 degrees. This range falls under the category of acute angles because all values are less than 90 degrees but greater than 0 degrees.
Therefore, [tex]$\frac{1}{2}$[/tex] of an obtuse angle is an acute angle.
The correct answer is:
C. acute angle
